The mouse controls while arm wrestling are so sluggish and awful that it is almost impossible to win - this really ought to be fixed in the next patch. Or is there a way to solve this yourself?

It's not sluggish and awful, it's meant to be this way in order for you to be difficult to keep it inside the bar. Do very small moves with your mouse and once you see it's on right track keep it as steady as you can. I've only lost to arm wrestling twice, after that i've beaten every NPC with the 1st try. It's not hard, you just need to work on it a bit -)

I've read that maximizing mouse sensitivity can be helpful. Didn't have to myself, but you might want to give it a shot.

It's really difficult on harder difficulty. If you feel frustrates lower it to easy and you can with just by twitching a little. Still hard if you lose the control once though. It meant to be that way I think sometimes it really feel like real arm wrestling!

Translation:

Waaaaaah waaaaaaah if I can't do something straight away it is impossible and/or broken waaaaaah waaaaaah.

I found the reverse true. I found it pretty easy with a lower DPI mouse setting, say around 400, which I can toggle to with a button on my mouse. Just try to keep it in the middle of the bar, so it doesn't escape when it shortens and suddenly reverses direction.

But people might experiencing issues with mouse lag or other FPS issues that are making it more difficult for all I know. Plus it's sort of tedious to move the mouse as if trying to snipe with a railgun for a minigame where something suggesting brute strength should be the order of the day.

You're right about the mouse lag. Disabling VSync might be helpful in that case.

About the "snipe with a rail-gun"-thing. I think it is meant to simulate the struggling and trembling muscles while moving inch by inch to one side. Quite a valid alternative to "hammer one key as fast as you can", as we don't have a way to input "strength" that I could think of.

You need to move slowly, steadily and firmly. Just like real arm wrestling ;)

Each system apparently is different I'm at 1300 dpi (Lower is more difficult for my setup) plus I have vsync on and my in-game sensitivity is low!! I guess experiment!! I think the problem with having options is too many options!! Like my children, instead of asking them "What do you want for dinner?" I learnded to say "Eat your dinner!"

geez i find the arm wrestling insultingly easy with the mouse, it seems to have inertia so if you move the mouse one direction quickly the indicator will keep sliding in that direction, i can usually just move the mouse 2-3 times and then leave it alone and the indicator will move at the same speed as the yellow bar it has to follow and i will win i don't even have to do anything else for the last 50% or so of the contest, in fact all of the mini games and qte's are just plain silly and far too easy.

What I am commenting is the fact that there seems to be no in-game support for a hardware mouse nor an option to turn of mouse acceleration.

I have no problems with the armwrestling games using the mouse.
As long as you make a good start and can keep the icon in the zone for a second or 2, then it's actually pretty easy to keep it there until the end.
It's when the marker gets out of it, then it gets really tough to recover and get the upper hand again, even if you were almost at the end.

Despite the absence of hardware mouse I find the arm wrestling to be relatively easy even on Hard (but I haven't finished the game on Hard yet, so we'll see). Using a 1000 dpi mouse. Yes, the interface is intentionally sluggish by design. As many has suggested, use small mouse movements because the motion drags on.

The mouse is sluggish, but it feels like it's supposed to feel that way. My trick is to keep the circle placed firmly on the left side of the bar, so if I get too much "inertia" going right, the circle has room to travel. In other words, don't try to keep it dead center. I've only lost twice, and that was after I took an Ambien. I play on normal difficulty, if that matters.

I managed to do the one in the tutorial just fine, but in the main game, not a chance. Moving the mouse doesn't actually seem to do anything anymore, the yellow bar just drifts to the left regardless of what I do with the mouse. I've lost the second the match starts. I'm sure I'm doing something wrong but I can't figure it out.