Steering adjustment?
 

While driving the boat (502/bravo 1 setup) when coming off the throttle the boat will hook to the left out of nowhere feels very unstable but i am able to get it back under control. Sometimes happens when I go on an angle across another boats wake. When I was talking to someone about it he said he has the same thing going on. Told me to raise the outdrive and he moved it from side to side saying there was too much play in it. He said I need a new transom shield which I have never heard of. It does seem to have excessive play 4 inches on either side. Thanks for any help

Sounds like it could be a worn gimbal ring.

How long can I let this go for? Not really in a financial position to fix anything major at this time.

beter yet is it safe to run it as long as I don't beat on the boat?

That would depend on how bad it is.

all the rams back there have big rubber bushings in them... if they fall to bits or the bolts loosen up the drives will steer all the hell over the place and do exactly this... look at them really carefully before you get hurt or break something badly.

i have seen this more than once.