I have a 2003 Acura TL and whenever I accelerate the car makes some kind of clunky noise that seems to come in the engine/trans area or maybe the front driver tire. IT only happens when I accelerate. Does this sound like a bad transmission? How should I troubleshoot?

1 clunk or a whole mess of clunking untill you get off the gas?

1 clunk i would look at motor mounts and exhaust hangers.

lots of clunking i would look into axle shafts wheel bearings and maybe the transmission.

My daughter has a 2002 cl. Acura will replace your transmission and provide a 110,000 mile warranty. No questions asked.
Call them and go to the dealer

i just had my 2003 Acura TL with 62k miles replaced under the extended
warranty but they want me to shell out money for front and side engine
brackets. Are these imperative? Shouldn't they have to pay since it was
probably caused by premature wear from my transmission?

no those mount do break down about every 75-100K
getting new ones is a good idea and in no way could these have caused your transmission to fail.

but they may have been the problem. and not the transmission.
BTW you should not pay any labor on the front 1 because they had to pull it to replace the transmission.

labor on the side mount yes if it is the left side mount but the right mount comes out with the trans.

IMO pay for the cost of the mounts (under $100) each
but no way in hell pay for the labor

and always ask "what would happen if i dont replace them"
and ask why did my transmission fail??
and ask can you show me my old parts and point out the bad piece and why it is indeed bad.

Ok i should of took everyones advice. The dealer replaced the trans under warranty and i chose not to get the engine mounts at the time. Now i feel the vibration and think its the engine mounts. The front and side are cracked. About how many hours of labor am I looking at?