I installed a Daikin mini-split in my shop two years ago and it works great.  We live in N. Texas where the summers are scorchers so it makes life bearable in the shop.  I saw something on YT the other day during a discussion using mini-splits and the comment was they aren't appropriate for a woodshop, I presume because of the high dust issue.  Has anyone who uses the same thing had any issues?  I'm thinking about purchasing a Jet or Powermatic air filter to help with that issue now that will be coming up on hot weather again.  Will that help?

Yeah, just pull the front grille regularly and clean the coils and filters.
I don't have one but know guys who have/had mini-splits in their shops. Its all about cleaning so the unit doesn't clog up.

Much better to invest into better dust collection and air filter like mentioned.

Where a clima unit suffers, your lungs suffer more ...

I've had a Sanyo 1.5T heat pump in my shop for 10 years. I clean it twice a year and I probably need to increase that to three times a year. It's not difficult just takes time. On mine I can program it to start/stop when I want. So I set it to run for one hour every day in the afternoon when it is warmest. Winter or Summer this helps when I don't get in the shop for days. It will keep it above 40F inside during a normal Winter so that nothing will freeze and below 80F in the Summer. If it gets too cold it will not draw any heat from outside but if it's that cold I don't want to be out there anyway. In the Winter I can turn it on and in an hour the shop will be in the low 50s and another hour will be nearing 60. If I had a bigger unit it would do better. I wish I could have gone bigger but limited by electrical capacity in the garage.

I put a mini split in my garage last year, and keep thinking it could help with air filtration. The Powermatic filter is on my short list, along with a roof vent fan for venting smoke and fumes. So when I have some free time long in the future I plan to build something like this guys filter box.

Edit: Weird, had issues with the youtube URL. It shows fine in Preview, but leaves a big white space on my computer. Oh well I tried...

I checked the filters last night and there was quite a bit of dust in them that I was able to blow out. It wasn't as bad as I thought.  However, while up on the ladder, I looked around on the top of my cabinets and florescent light fixtures hanging down and they were covered in a thick layer of dust. I got that taken care of and now I'm going to get one of those air cleaners to help keep it from ever becoming this bad again. 

I installed a mini split and a 4 filter top box  after I saw the idea from Jay Bates on YouTube.  Between that and 4 hanging air filters I made from some old mini split fans (courtesy of a buddy who installs air conditioning systems) I have had zero problems with it.
 I checked the filter on the mini split about a month ago when I changed all the filters for the first time and it was clean as the day I installed it. Jay's idea with the 4 filters is fantastic, and works very well.

The only downside to them I was told is that while they are great for AC they are less than desirable for heat especially is cooler climates. It's a heat pump, which means it cannot do the job without heat strips if it drops below 45 or so. If your shop is in a garage and you live in a cold climate the mini-split with struggle to heat it. The door is a sieve for cold air making it tough to warm up and if the door is opened it will be game over for a mini-split using it's strip heat. This is where a propane wall-mounted unit could take care of business.

I suffer in the summer in my garage, but propane powers me through winter.

The only downside to them I was told is that while they are great for AC they are less than desirable for heat especially is cooler climates. It's a heat pump, which means it cannot do the job without heat strips if it drops below 45 or so. If your shop is in a garage and you live in a cold climate the mini-split with struggle to heat it. The door is a sieve for cold air making it tough to warm up and if the door is opened it will be game over for a mini-split using it's strip heat. This is where a propane wall-mounted unit could take care of business.

I suffer in the summer in my garage, but propane powers me through winter.

That is no longer accurate.
There are low temperature units available that can produce effective heat from -15° F air, which do not use any sort of resistance strip heating.
I had one installed in my NH house coming up on two years ago. It works extremely well, it keeps our 1800 sq ft house more comfortable than the propane furnace it replaced ever did, and the running cost has been a fraction of what the furnace needed. That it also cools or dehumidifies is a bonus, but we bought it primarily for heat.
-15 is rare where our house is, but low temps between -5 to -10 aren't unusual and the mini-split is able to keep the house comfortable throughout. We also have a wood stove, and run it sometimes in the colder times to augment, but doing that is entirely optional, and the stove's primary role is to provide heat if there is a power outage.

And, yes, I needed a bit of a leap of faith before I made the decision to buy it.