I have a dewalt DW368 Circ saw, which has problems making square cuts because the baseplate flexes allowing the blade angle to change. Is this a known problem? I can easily flex the baseplate 1/8" side to side.

bent --blade--arm-//bearings -blade shaft --shim or holding plate and bolt ///arm --shim--washer - bushing -bolt worn or damaged

Did you check to see if the saw has a locking nut on the front of the bevel gauge handle? Its possible you just locked it into position and forgot to unlock.

Few budget tools and especially generic, brand engineered tools imported from the far east are superbly accurate but tend to be "near enough".

You didn't say whether it is a hand operated mitre saw or a power saw.
Most power mitre saws have a number of stops that can be adjusted or filed in order to calibrate the angles and this process should be done when the saw arrives. Once both 45 degree angles have been calibrated accurately the angles in between should fall into place fairly well.

One problem with low cost mitre (chop) saws, even some so-called professional saws is the construction is so light, when pulling down the handle the machine flexes and spoils the cut. This is especially true when the handle is not set exactly in line with the blade or when not paying full attention when making a cut.

Having experienced such saws I have learned much about them so when I visit a tool store I examine their stock by twisting, rocking and pulling the saw heads and the amount of movement in many new saws of popular brands is disgusting, even some pretending to be premium brands. So far only a few of the most expensive types have impressed me.
That doesn't mean the others are unusable and with care fairly accurate cuts can be made when a suitable technique has been developed - like using a rifle with bent sights...

Make sure the blade is 90 deg vertical to the saw table. Make sure the indicator is set approprately. Raise the blade just enough to clear the table/base. Place a swanson speed square against the fence and blade. Make sure the indicator is at 90 degrees. Here you might want to tilt the square and check that the complete blade is flush against the sqaure as high up as possible. Lay the square back flat on the table and pull the blade toward you as much as possible. The teeth on the blade should ride against the square extented completely out.

Now set the square against the fence with the 45 degree angle coming away from the table and set the blade on the 45 deg mark on the insicator scale.
The blade should touch the square all the way out fully extented.

Or just experiment with some scrap and check

When you are facing the front of the table saw. Right above the Dewalt logo, there is a hand wheel that if you crank clockwise - it will tilt your table saw blade to the angle shown where the hand wheel is.

Narrow throat plate should work. Sure you have the blade installed correctly with arbor washers?

There shoul be a scale and a crank or screw used to adjust the blade angle on the front of the saw blade feed bushing. Make sure you set this to 90

User manual for adjusting your saw here.
When you set it up, make sure you check for square to the table, square to the fence, and check square for toe-in or at a 45 deg. angle across the blade from the corner where fence meets table, like you would check a radial arm saw. (hold a framing square with one leg against line of fence/table and other leg against blade and inclined 45 to both table and fence. Make sure all three are dead square.
I never found any way to compensate for the play in the blade itself. It seems like the manufacturing tolerances are a little too loose.

You may need a heavier plated blade. You may simply need a different saw. Those Dewalts are great workhorses, and I love the design, but it's my experience that when you're trying to miter hardwoods of any substantial size there's a little bit of drift in the cut as the blade comes through the wood.
You can try cutting at a slower rate.
I've found that makitas are a little more solid through the cut, though I don't like the general ergonomics as much...
Kind of a pain, isn't it?
Well, good luck.

I hope this information allows you to resolve this issue. If you need further assistance, please post back with a comment to this thread.
If I've managed to answer your question or solve a problem, please take just a moment to rate this post....thanks!

Inside the saw, on the end of the trunnion is a stop that is adjustable to zero the saw in to exactly 90 degrees. Either there is sawdust or something accumulated there or it needs to be adjusted. You say you cleaned it out, So you'll need to unplug it an have a look up in there. See how there's a geared piece of steel that moves when you crank the saw over to 45 degrees. Usually there's a bolt or stud with a locking nut on it, either on the trunnion itself or the lower surface of the table top. You need to break the nut loose and screw the bolt in or out to adjust, then crank the saw over to hit it, check for square with a known square, crank it all the way out of the way and readjust, etc. Until you get it right. Make sure to tighten that lock nut when you're done.

I hope this information allows you to resolve this issue. If you need further assistance, please post back with a comment to this thread. If I've managed to answer your question or solve a problem, please take a moment to kindly rate this post....thanks!

The bearings in your saw need to be replaced. I would contact a DeWalt store to obtain the parts or have them do the repair. You have an excellent saw there, well worth repairing. good luck.