When driving I can feel the bottom front part of the seat lifting up and moving in the middle. Is there a nut that can be tightened that I can do myself???

 

Could be a loose bolt but more likely play in the power adjustment mechanism (not adjustable and prohibitively expensive to replace).

 

Now why would you go and say that? I've recently noticed a little play in both front seats of mine

Is this a common problem?

 

I didn't have the problem on my 2007 or 2014 LS but did have it on my BMW and it was just awful - the most comfortable setting of the seat coincided with the greatest play in the seat mechanism. Every time I acellerated, the seat rocked backwards and every time I braked it rocked forward. The BMW dealer replaced the entire seat frame but it wasn't much better. I ended up driving the car for 13 years with the seat jammed down in the lowest position to eliminate the play.