Yes, it is also a good idea to remove your selected skills when speaking to a trainer, only selecting that particular skill you want to train. For example, if you speak to a lockpick trainer, prior to paying to have your skill boosted make sure that is the only skill selected at the time (This applies if you are grinding any skills as well).
If you tag too many skills then your chance to increase each additional skill decreases by X%. I am not sure what the exact percent decrease is.
