I always feel a little bump right after taking off from a dead stop when towing my boat. I noticed that I could move my hitch in and out of the receiver about 1/8 - 3/16". I bought a new pin and hitch and it was exactly the same. It seems the hole in the hitch itself is fairly large for the 5/8" pin. I checked all three of my receivers and they were all like this.
Is there supposed to be this much play?

Does your trailer have surge brakes? If so, look at it like this.

Let's say you have a small amount of play in your ball mount and pin. Perfectly normal. Compound this with play in your surge brakes and it will feel like your trailer is moving about a foot or so from the driver's seat.

If your hitch is in good shape I wouldn't worry about it. I see this a lot. Some tend to make a bigger deal out of it than it really is.

Just make sure all of the items in the process are in good working order.

Buck

mine feels the same way, feels like it could snap your neck if you forget to take offf slowly

Normal operation

i have the same deal.

Perhaps a threaded bolt through the pin hole would be better?
Also, maybe drilling a hole through the receiver vertically in front of the drawbar, and insert a bolt vertically that would provide a positive stop for the insertion of the drawbar.

Make sure the parts that slide on the trailer surge brakes are always well lubricated so that they move freely. I have found that if you stop, then inch up a foot or so it will remove all the play and then when the light goes green you can hit it without worrying about the big whack when things get pulled apart.

They make a special pin to tighten the reciever up to stop this you can buy it at any trailer dealer its about 24 dollars

Actually- this would not be wise- a threaded pin has way less surface area and will wear all the holes quicker- when we mount rod end links in the race cars we go out of our way to select/make bolts that have a full shank through the rod end itself and the double shear plates on each side.

To correct worn holes you can get or make a 5/8 weld washer (say 1/4" thick) and assemble the unit- then weld the washers in place to restore the worn holes

The vertical pin is also not the best idea- the existing horizontal hole is located in "the neutral axis" of the 2x2 or 2.5" tubing- makes no difference in the bility to handle load.

The metal in the top and bottom of the tube are doing all the work- weight wise- punching a hole in the top and bottom would compromise the designed/intended strength.

EDIT- just reread and realized you suggested a mechanical stop made with a hole drilled only in the female part- would not be as big a deal- but still relavent- the weld washers would likely be easier and more effective though

As said- they do make some special antirattle type ballmounts- just make sure they are rated for your load.

The effect of the cummulative slop is usually magnified in a marginal towing situation where you have barely enough truck- you just plain feel it more

Its the trailer surge brake....in normal operation it does this.