On a liner lock, any up and down play indicates that there is no tension between the back of the blade and the locking bar.This is a sure recipe for having that locking bar swing out of the way and letting the knife fold up, always at the worst possible time. If you look carefully at the point on the back of the blade where the locking bar makes contact, you will see that it is slightly angled to create a binding effect as the bar hits it. That tension is essential to the correct function of the lock. On a well made lock, as the moving parts wear, the farther the locking bar will travel across the contact point, insuring that tight lock up and tension remains. If you have a liner lock bar that goes all the way across the gap to the other side of the liner, your knife is either worn out of tolerences or was never right in the first place. Either way, it needs to be repaired or replaced. When I say replaced, I mean the offending knife should be disabled or destroyed! It is a hazard and should not be handed down to some one else or sold to the unsuspecting.
Side to side wiggle offers another potential problem. The side to side movement can create a ratcheting action between the locking bar and the contact point. The back and forth movement will slightly push the locking bar towards the point of disengagement in very small increments. If you are concentrating on the task at hand, you won't even notice the movement. Once again, the recipe for the knife folding on your fingers is there.
Wiggle on either axis will only get worse with time. It will not self correct. That is why it is so critical to start out right.
People have asked me I'll spend so much to buy a given knife. I'll explain that while I may have spent $100-$200 for a good production folder, the cost of surgically re-attaching severed fingers is about $10,000 per digit. Sure makes the upfront cost of a good knife a bargain!

90% of the time, my EDC is an Axis lock. I am habituated to it's method of carry and I have absolute confidence in it's lock up.
Dave