It is difficult to prove a negative (that Britain did not intentionally create problematic borders), but there are good reasons to believe that there was no conspiracy to create problematic borders. To support my claim, I mainly draw upon an excellent summary given by Chester, and the "Problems in the process" section of the Wikipedia article on the Radcliffe line. Notably, Chester has since written a book on this subject, which I have not read.
The border demarcation was done by two commissions, each chaired by Sir Cyril Radcliffe, and each commission contained two representatives from Indian National Congress and two from the Muslim League. Since Congress and the Muslim League had generally hostile relations and were typically deadlocked, the decision-making power rested with Radcliffe. If the British government conspired to create problematic borders, then either 1) Radcliffe would have known and implemented the plan, or 2) the British government would have intentionally created a situation in which the commissions would fail to properly demarcate the borders. Radcliffe destroyed all his papers relating to the commissions, but we have information from other sources on how they were carried out.
If Radcliffe was in on the conspiracy, he could have made things worse. Few would argue that the borders were not problematic. However, if Radcliffe wanted to sow discord, he could have easily drawn borders with no regard to current boundaries, but he generally adhered to current administrative boundaries.
The borders were drawn far too hastily, causing many problems, but all parties insisted on this. Soon after Radcliffe arrived in India on July 8, 1947 to setup the commission, he learned that the commission had to be complete by August 15. He protested, but the British Government, Congress, and the League all insisted that the work be complete by that date. All three parties had their own political motivations: both Congress and the Muslim League wanted to take power as fast as possible, while a war-weary British government wanted to divest themselves as quickly as possible. If the British did desire to hamper the work of the commission by imposing an unrealistic deadline, they certainly would not have had to work hard to convince Congress or the Muslim League.
The evidence suggests a lack of a coherent plan, inconsistent with a conspiracy. Neither Radcliffe, Congress, or the Muslim League had any advisers specialized in the establishment of boundaries, despite the fact that they existed at the time. Radcliffe had never visited India before, but had to make all the decisions himself. As Chester notes:
The commission’s membership, composed entirely of legal experts,
hampered its boundary-making effort but added a valuable veneer of
justice and legitimacy to what was, in reality, a chaotic jumble of
The British government did not have much to gain from sowing discord through hastily demarcated borders. Both countries were to be members of the Commonwealth after independence: presumably, Britain was interested in the stability of Commonwealth countries. Chester notes that Radcliffe assumed that Pakistan and India would have good relations after the division. Indeed, Radcliffe notes that the use of some of the infrastructure which was now located on both sides of the border would have to be negotiated between the two parties.
Lastly, there were many causes of the postcolonial disorder. I liked this quote by Mishra:
Many of the seeds of postcolonial disorder in South Asia were sown
much earlier, in two centuries of direct and indirect British rule,
but, as book after book has demonstrated, nothing in the complex
tragedy of partition was inevitable.
Perhaps the British decided to "push the disorder along" by conspiring to setup a commission bound to fail. But the alternative is at least plausible: the British wanted to find the most politically expedient way of quickly divesting themselves from India, and found that Congress and the Muslim League were happy to see them go as quickly as possible. The only obstacle to independence was the drawing of the borders, which was then done as quickly as possible, creating turmoil that would last decades.
I realize that I have not answered the second part of your question, "Was this done with other countries?". I feel that the scope of the question is too broad to be answered properly. The difficulty in answering this question for even Pakistan and India makes it clear how difficult it would be to answer for all other countries.