The causus belli of the First Gulf War was the Iraqi invasion of Kuwait. President George (HW) Bush managed to get a series of UN declarations calling for the Iraqi troops to leave, and authorizing succesively more drastic actions to achieve this, culminating in 678, which authorized "all nessecary means". This provided a certian amount of international cover for military action, but only towards restoring Kuwait, not toppling Iraq itself.
Also, many Muslim states signed on to the effort as allies, with the understanding that the recovery of Kuwaiti independence was the only goal. Most significantly, Saudi Arabia provided the required miltary basing and staging territory, with the understanding that the scope of the effort was limited to restoring Kuwait.
There is debate about whether the US administration would have liked to see Saddam toppled as well. Colin Powell claims in his memoirs that the intention was always to leave him in place, as a bulwark against Iran. However, various public statements made by President Bush led many people inside Iraq to (incorrectly) believe the US would support popular uprisings, with very unfortunate results. The administration of his son (GW Bush), certianly believed this was a mistake.
As to Iraqi failures, frankly they lost the war the instant it started. Their mid-20th Century vintage Soviet and Chinese military hardware was simply no match for modern top of the line US and NATO equipment. They could have been tactical geniuses throughout the conflict, and still gotten beaten handily.