"Are there a lot of issues with non-competes?"
What would constitute "a lot"? The last few years I've seen an increase in the tech industry of non-competes being required for less senior roles, plus reports of using non-competes in low-wage industries to try to freeze workers from leaving jobs. [1]
They're also over-broad and selectively enforced. I was considering a job last year that had a non-compete and wasn't eager to sign it because if you read it broadly it would've been hard for me to take a job that wasn't with a "competitor." Which was 1) over-broad and 2) bogus because the harm that would've been done to me was far outsized to any harm I could've done taking a job with any competitor.
I wasn't going to be such a strategic employee that me going to Company B would have hurt Company A in any real way (nor would I have been compensated at that level...), but I was expected to sign a non-compete and be severely restricted in my next job options -- or roll the dice and hope if I took a job with Company B later on that it wouldn't be considered "a competitor" or that the employer would care.
And that's the other problem - I was told by several people "eh, that's not enforced" but it was not something they were willing to forego, either. I don't sign agreements with the intent I'm not going to live up to them. It's not reasonable to have that kind of uncertainty, either.
Non-competes have their place - I can see, say, Netflix putting in place a NC with a head of programming or major cloud providers having non-competes for very senior execs who have extensive information about strategy, budget, customer lists, etc. But lower-rung employees who don't even have their own budget or any material knowledge about the operations of the business? That's stupid.
[1] https://www.mashed.com/620419/the-contract-you-didnt-realize...