Quoted from Rdoyle1978:Ok first of all - I would completely disassemble the bracket so you can clean it up. The grease they used way back in the day turns into a hard clay and will definitely
Impede movement.
After that, the bracket that goes across the back is what can be adjusted. But you should also use a T- or L-Square to check that the bracket hasn’t bent. When the rear brace goes out of alignment, the whole thing gets bent. You may need to gently re-align it. Then tighten that rear bracket.
Now before you do any of this go read the best guide about the doctor who MPF: Faz’s guide. It’s in the official DW thread
All of the above, and that play looks about normal for the game. That whole mech is a royal pain in the ass. I've spent a ton of time on mine and a friends to get the movement as close to perfect as you can with the original stuff, and I honestly have come to loathe the game because of it.