The 360 is just fine for watching standard dvd's. No need to buy a seperate dvd player unless the 360 breaks down and you don't get it fixed. As to your issues, the audio cutting in and out could be due to a faulty HDMI cable. As to the problem with the 360 occasionally having problems reading dvd's is that the dvd drive could be on its way out or eventually the RROD. You might be still be covered under the extended warranty depending when you purchased it.
Do any error messages appear when it does not read a disk? This is very important.