One thing that was annoying is that you have to be careful on where you start building when you're going to build to a wall, because if you start building on the wrong spot, the Lemming will bash the stair and fall instead of bashing through the wall. This was fixed in the PSP. You can even see when it's ok to start bashing, because after the Lemming has placed the step, the pixels of the step changes and that's where you can start bashing the wall and not destroy the stair.
The explanation for the described known problem in "classic" versions of the game (ie. PC, Amiga, etc.) is slightly incomplete. The real issue is that depending on where you start building (and in some cases which direction the lemming is facing), the player may never be given a chance to carry out the desired bashing behavior--too soon and A) the game still considers the lemming to be standing on the old brick rather than on the new brick just laid, so when you bash you fall, but too late and B) the game already executed the "turn around on wall" behavior, leaving you unable to bash in the desired direction. There exist not-uncommon cases in the classic version, depending on where you start building etc., where the player will always be either "too soon" or "too late", hence the problem.
It sounds like in PSP, they addressed this problem by making sure there is always a safe period of time between "too soon" and "too late", perhaps by treating the lemming to be already positioned on top of the new brick just laid, even if the animation of stepping up onto it is still ongoing (at least that's what your description sounds like, I'm not sure). Basically by putting more forgiveness with respect to A. One other alternative is more forgiveness with respect to B, ie. don't trigger the turnaround behavior until lemming is
really close to the wall, rather than just barely close enough for the build-bridge to connect to the wall. Another alternative is to always provide a small period of grace between "lemming finished moving up onto the new brick" and "turnaround behavior executed".