Is it 2-head or 3-head ? Asking cause if it's 3-head, playing fine just means the playback head is OK. Recording head maybe isn't. Also are the heads clean ? A dirty head can be quite forgiving on playback. That doesn't happen with recording.
How the heads look ? Marks, dots ? If you see a mark on head's gap, then head is dying if not dead already. The best way to check a playback head's performance is with frequency response test tape. But these tapes cost quite a lot, and only technicians really need them. A DIY test i have read -if i recall correctly- is record a 100Hz test-tone and a 10KHz test-tone of the exact same level on a deck you trust. Then playback them on the deck in question. Are the two test-tones have the exact same level ? Then head it's still in acceptable condition. The higher the flat response, the better. For example good decks have specs 20Hz - 20KHz response [+ / - 3dB] , for the most part flat and the possible deviation happens as we getting closer to the limits. Where it starts i have no idea, i guess it depends. Anyway, an average deck has specs 30Hz - 16KHz or 30Hz - 17KHz [+ / - 3dB] with normal tape. The 100Hz - 10KHz is the "main body" of that range, so a good condition head must have really flat performance in this. Otherwise it's useless. How much deviation is normal there ? Hm, i don't know. Ideally no deviation ! That + / - 3dB is normal only for the full range !
I am not sure how you can check recording's head performance. I guess by recording test-tone covering all the frequency range, and playback it to see if it was really recorded according to its specs. But then again you need to know how the playback head performs so you know your results are valid. I don't know ...
Last but not least, the problem you describe maybe isn't cause of bad head. Head is only a part of that chain.
Edit : I made a correction. The two test-tones better to be recorded on the same tape.
Edit 2 : Added some explanations more, the italicized text. I want to be as much accurate as i can.
