A computer that can manage the TNG holodeck will have no problem handling all the complexities of a transporter.

Plus it needs to identify what creepy crawlies are a part of you and which were just randomly wandering by.

It does do that. It's canon that transporters take care of removing any foreign organisms.

And how does it know what clothes are? If I'm wearing shoes, does it know where the shoes end and the floor starts? What if I'm wearing skies? What if I'm barefoot on a carpet? What if it's a leather carpet? What if I'm wearing shoes made by folding carpet around my feet?

It understands all those scenarios and relays them to the operator, who decides what to lock on.