If I remember correctly from the PS3 version (and also noticed in the Remastered version). There are certain areas that slow your walking/sprinting down, most likely to keep up with the NCPs or listen to their conversations. There are parts of the game that 'feel' like they should be slowed down, like when there's no combat and not much of a threat around, it wouldn't make sense to always be running in real life.
Unless your talking about something totally different (a glitch), I think the game was meant to do that to give it a more realistic/cinematic feel.
Im having the same problem also. As so as I started using Sarah I noticed that something was wrong. It took me like 5 minutes to get down the stairs, because she kept doing this shuffle. What is weird though, is that when you move left and right, at least for me, the movement is ok. I hope they fix this soon, because it really breaks up the beauty of the game when you just keep doing the harlem shake.
Posted on another thread like this but it seems to be a controller issue - maybe....
I remote played from my Vita and have no issues. Switch back to the controller, and the issue arises again. So, I just ordered another controller from Target ($10 off with store pickup) and will write back with results.