I'm going to draw heavily on United States Army in World War II
The Western Hemisphere - Guarding the United States and Its Outposts. I would argue the US Army was very quick to adopt radar, just a few years, but events unfolded faster than they could fully integrate their lessons.
Rapid Modernization and Expansion
In 1941, the US military was still undergoing a rapid modernization and expansion started just a few years before. Everything was being upgraded. New equipment was just being delivered. Everyone was having to very rapidly adapt to the new technology and tactics of WWII. Not everyone adapted well. This report on the state of the Panama Canal defenses lays it all out.
The recurrent crises in Europe during 1938 made the weak spots in the defenses of the Canal seem glaring indeed. With respect to antiaircraft, coast artillery, and air forces, the situation was particularly acute. The actual strength of the two coast artillery regiments was inadequate for the proper manning of the seacoast defenses, and as a result the infantry troops had to be given double assignments and dual training. The existing system of fixed antiaircraft batteries lacked, it was believed, sufficient depth and mobility to offer an effective defense against high speed, high altitude bombers. The air force was equipped with obsolete planes. France Field had been outgrown for some time, and room for expansion was lacking. The main runway of Albrook Field was still under construction. Moreover, it had become increasingly clear that by the time hostile planes came within range of the existing Army defenses it would be too late to prevent them from delivering an attack on the Canal. Effective air interception would require long-range patrols, radar installations, and a screen of outlying bases. Not one of these requirements was available.
Source: Chapter XII - Forging the Defenses of the Canal
General Short started his military career in 1902 with horses, runners, and bolt-action rifles. The anemic interwar US military budget meant his experience would stay that way for far longer than other militaries. Now he's overseeing machine guns, radio, motor transport, tanks, aircraft, and now radar. It must have been dizzying to keep up with and assimilate all the new technology into his thinking. This was the pattern for US senior officers.
Radar was brand new. Its potential to be a decisive factor in an air battle was only just demonstrated in the summer of 1940 during the Battle of Britain. The US had a little over a year to react.
The first sets of SCR-271, the air early-warning radar, were installed at the end of 1940 in Panama to get their first real use in the field. The junior officers operating these sets went to a brand new air defense school in April 1941 for training and to be taught the lessons from Britain, but the senior officers did not. As a result, radar was poorly understood at the command level and poorly integrated into air defense.
Sabotage
Pearl Harbor was primarily concerned with sabotage, yet still put the brand new radar on alert.
General Short's action had been to order an Alert No. 1, as defined in a new Standing Operating Procedure dated 5 November 1941. This alert assumed increased danger of sabotage and internal unrest, but no threat from without. Under it the Army, in General Short's words, "put out a lot of additional guards and checked on everything," and for the two infantry divisions this meant keeping thirty officers and 1,012 enlisted men on guard and patrol duty. The Hawaiian Air Force was ordered to concentrate planes so that they could be guarded more easily, and these orders were as easily executed since that was the usual practice at Hickam and Wheeler Fields anyway. The only deviation from procedures prescribed under Alert No. 1 was an order directing the operation of the new Army radar machines between four and seven each morning--the most likely period for a carrier strike, according to previous studies.
Source: Chapter VII - The Pearl Harbor Attack
Keep in mind that at this time, carriers were still very new and mostly untested. The British had demonstrated the actual power of aircraft against ships in harbor at the Battle Of Taranto and that lesson was still being absorbed. There were so many other targets between the Japanese home islands and Hawaii, and the war hadn't even started yet, that an unprecedented massed carrier strike at Pearl seemed a very remote possibility.
When first questioned, General Short said he ordered Alert No. 1 for three reasons: first, he thought there was a "strong possibility" of sabotage, and he feared sabotage more than anything else; second, he had no information about any danger of external attack; and third, either No. 2 or No. 3 would interfere very seriously with training--"it was impossible to do any orderly training with them on."
...
During the conference on the 27th Admiral Kimmel turned to his War Plans officer, Capt. Charles H. McMorris, and asked specifically what the chances of a surprise raid on Oahu were, and the answer was "none." No one of the other Navy officials present challenged this judgment, and General Short saw no reason to question it. Both he and his naval colleagues were also heavily influenced by the knowledge that Japan could not attack Oahu with land-based planes, and by the continuing assumption that the Japanese would not risk a carrier strike as long as the bulk of the Pacific Fleet was in or west of Hawaiian waters.
Source: Chapter VII - The Pearl Harbor Attack
Army/Navy I-Cannot-Put-Enough-Quotes-Around "Coordination"
The US Army oversaw the defense of Hawaii, but Pearl Harbor is a US Navy station. This lack of a unified defense for Hawaii meant two split command chains who would communicate and coordinate with each other only slowly and begrudgingly. This is an unfortunate reoccurring theme throughout military history.
The Navy was responsible for seaward defense of the island. The Army was responsible for the land and air (the air force being the Army Air Force).
Whereas the directive of General MacArthur to undertake reconnaissance was a sensible one, since that was at least partially his responsibility, it was not applicable to General Short's situation, for seaward reconnaissance to any meaningful distance was recognized in Hawaii as strictly the Navy's business.
Source: Chapter VII - The Pearl Harbor Attack
The Army operated the radar sets, but the Navy knew what was going on at sea. When a midget submarine was spotted hours before the Pearl Harbor attack by the Navy, nobody thought to tell the Army.
On Oahu the military forces did obtain other warnings of impending action. More than four hours before the air attack began, one of the midget submarines was sighted less than two miles outside the Pearl Harbor entrance buoy, and either this submarine or another like it was sunk near the harbor entrance at a quarter to seven. According to standing orders, the presence of any unidentified submarine in restricted waters was to be considered a warning of imminent attack on a larger scale; but the Navy was still in process of checking the authenticity of reports of these submarine actions when the big attack came. No one thought to tell the Army about them.
Source: Chapter VII - The Pearl Harbor Attack
The rapid introduction of new technology without training the senior officers responsible for its integration, the Army's focus on sabotage, and the lack of a unified command meant that when the strike was detected by radar there was no urgency to report it.
On Oahu's north shore, three Army mobile SCR-270 radar sets were in operation this Sunday morning, from 4:00 to 7:00 a.m., in accordance with the schedule established under Alert No. 1. All three (Kawailoa, Opana, and Kaaawa) recorded the approach of two Japanese reconnaissance planes, launched from cruisers, when they were about fifty miles away, beginning at 6:45 a.m. One of the stations (but not Opana) reported this flight to a Navy lieutenant on duty at the Army information center at Fort Shafter about 6:52 a.m., who reported it to another Navy lieutenant who responded that the Navy "had a reconnaissance flight out and that's what this flight was." Much better known is the report by the Opana station at 7:20 a.m. of a mass flight of planes approaching from a northerly direction. This was the first wave of Japanese bombers and fighters, which had been spotted by the Opana radar just after seven while still some 130 miles from Oahu. By the time the Opana report came in the information center had officially closed down, and an Army lieutenant who happened to be still on duty decided that nothing need be done about the call--he knew that American carriers were out and assumed that Opana had picked up a reconnaissance flight from one of them.