I would like to know if there can be reading/writing problem because the heads are unclean,
or that the plates should be cleaned and reassembled.
Not really - while it's true hard drives are not 100% air-tight, any openings in a hard drive case are covered with a very fine filter that prevents particles of any size from entering the case. There is also, I believe, usually a secondary backup filter inside the case (haven't taken one apart in a while, so not sure if that's true every time).
As to taking it apart and cleaning it, without a clean-room, you could not possibly get it cleaner than it already is. I won't say that taking apart and re-assembling a hard drive will destroy it 100% of the time, but it's very,
very likely you'll wreck the drive. Touching a hard drive platter with anything would spell the end of the drive for sure.
Bottom line: if you have a destroyed hard drive, that is utterly unusable, you can take the drive apart for fun (the magnets inside are pretty powerful), but taking apart a working hard drive, for any reason, will almost assuredly guarantee you an expensive paperweight.
Cheers!
regnak