If you had a friend do it, find out how much of a friend he is by telling him about the problem. If it is a business and they deny you service, the BBB is out there for filing claims against companies with bad business etiquette. Never have work done professionally without a warranty. Even junk yard transmissions have a 30-90 day. Rebuilds generally carry a 1 year. The first thing would have to be transmission compatibility. In most newer vehicles, not only does it matter what the bolt pattern is, but it matters what the torque rating is. If you installed a higher output engine in front of a standard transmission because forums said it is possible, that's where the mistake is.
I'd agree with Tim partially, with exception to actual parts found in an automatic equipped vehicle. Though it would be highly unlikely they would forget to install the "flexplate", it might be try that they could forget to bolt it to the torque converter. However, you'd definitely hear the torque converter hit the bellhousing.
Being any sort of mechanic, whether it be diesel, construction, gasoline, etc., I would expect one to first say that it is very likely they damaged the pump when they installed the transmission. Either by not filling the filter, the torque converter of topping off the transmission with fluid. This is all too common and when it comes to FWD vehicles, and confined engine bays, it is very likely suspect.
Stripping gears would be near impossible in an automatic. Fluid transfer is responsible for everything. It's what controls the valve body and the valve body decides what clutches and steels are engaged. The only gear you might hear is the park mechanism when you accidentally put the vehicle in Park before it comes to a complete stop.
-edit- new reply: KrazyBob613...
... might be dead on if not close. The plastic retainer that holds the cable to the tranmission linkage/selector might have popped off. All too many times when the lock is removed, it breaks and the shad-tree mechanic installs the clip without a lock. If it is a cotter pin that locks it in, it should have been replaced. Often they break where they've been bent, once they've been bent again.
If a dealership preformed the work, they will warranty it if the damage is found to have occurred during/from installation.