There are a number of 'irregularities' that have been suggested/identified - not all of which have been explained, or at least to the satisfaction of the doubters. Just some of them are:
The difference in temperature between burning aircraft fuel and that required to melt steel girders. Also the relative difference in tensile strength between girders designed to support immovable skyscrapers and the body of an aircraft designed to be as light as possible to fly through the sky;
The discovery of an intact and identifiable paper passport(s) in the wreckage where metal and bricks were burnt to a crisp;
The nature of collapse of the buildings, which some have suggested more closely resembles that of a controlled demolition explosion;
Building 7 completely toppling in the aftershock of the destruction of the twin towers - which was reported as having happened by the BBC, 20 minutes before it actually seemingly did;
Claims that highly-experienced senior military pilots have cast severe doubt on their own ability to complete such a precise manoeuvre at the same speed as was executed successfully by novices who'd had a few lessons in flying a plane;
Claims that the owner of the buildings had taken out an extremely valuable insurance policy specifically against the towers being the object of a terroriost attack, only a very short time before it happened;
Also from a cui bono perspective, the Patriot Act was rushed in almost immediately - a lot of Americans are deeply unhappy about the perceived disproportionality of its restrictions on their civil liberties, as well as surprised at how very quickly it was all drawn up, finalised and ready to enact.
I've also heard of murmurings about a document called something like 'Plans for the New American Century' and alleged quotes that 'a new Pearl Harbor would be necessary', but I don't personally know much about that avenue of claim/research/evidence.