When should you avoid it?
Well I wouldn't start off a chorus with it. You can though.
It really depends on the situation and style of music you are playing.
Generally, if you have any sort of (i'm going to use Solfeggio here, be prepared) Fa to Mi or Me realtionship, it's totally cool to play the third on beat one, in fact, i think after playing (assuming you are playing a ii V I (or i) the seventh of the Five chord on beat four it's almost nessicary to go down to that third.
Or at least that's what I hear.
The walking bassline is all about motion, so really it just depends on how you get there and where you are going. If you have more disjunct changes like in say... "the sorcerer" or "fee fi fo fum" you can still use voiceleading knowlege. If I were you I would study counterpoint. Counterpoint is awesome.
I don't know if you've heard of Ben street, he's an amazing bassist, and all he studied in grad school was counterpoint, and his basslines and solos are amazing.
But then, you have to keep in mind, the whole point of learning anything in music is to make music.
Everything in theory is after the fact. Music is heard, not written. When you say "when is it appropriate" it's really compleatly dependant on your ear.
If you do it enough it will start sounding right, and then it will allways be appropriate.