Too many to even mention. The example you cite (I play piano) is acceptable since a piano is an object. If he were to have said "I play THE baseball" that would be confusing, because baseball is a sport/activity and does not need a "the" beforehand. If you play THE drums, or if you play drums, it's acceptable. If you run track, that's acceptable. It would sound odd to say "I run THE track" since track is a sport. It depends on the situation. If he had said "I drive car" instead of "I drive THE car" that would be unacceptable. Now, he could have said "I drive cars" in a plural sense and been correct.
The misuse of the word "that" in English is another pet peeve of mine. I have very limited understanding of Japanese and do not know if the word "that" is used often. But it is certainly overused in English.