In your case, where the glue has smeared, I would wither go to your local plastics supplier and get a plastic polish. The glue I use melts the plastic, bonding the surfaces.
Cutting 1/4inch can be done several ways.
If you have a table saw, a fine tooth blade will provide straight rips, however they will have to be sanded and finished.
If you have a jig saw, get a 15-20tooth blade, setup a guide so that the cuts are straight. Free hand is easy also, but in both cases GO SLOW
Use a variable speed jigsaw, and use low rpms as to not melt the plastic.
Now If you have a dremal, nothing works better then just a good old re-enforced fiberglass cut off disk. Set the dremal to 15-20k and make sure you have a straight like to follow. Start cutting at one end and move your way towards the other. Some people like to run the disk over the line, I dont do this because you have a greater chance of the bit jumping and scratching the plexi.
Best of luck