The only restrictions I've seen are that the drive must be mounted within 10 deg. of vertical or horizontal, and Seagate used to prohibit mounting with the front pointing straight down, both reasons probably related to head arm counterweight balance.
Vertical mounting is a good idea for cooling purposes if you don't use a fan, especially for some of the chips. I once mentioned measuring a Maxtor chip at 68C when the drive was horizontal, 53C when it was vertical, tests done on the bench, ambient about 25C.
It's a myth that orientation shouldn't be changed later on. That may have applied to old drives with stepper motor head positioners and no track servos (and not that much even with them), but all drives made in the past 10 years or so have servos, which automatically compensate the head positioning for wear and temperature, and Winchester drive ball bearings have always been the preloaded type (oil-pumping sleeve bearings in some Seagates and Quantums may be another matter), meaning no slop and no restrictions on orientation.