My Mom has been in a long term care memory care facility for just 2 months. My Dad wants to bring her home for a weekend. Thoughts?

Imho, bringing her home for a weekend would NOT be as good decision. Upon return to the MC, your mother would experience confusion and possibly disorientation.

Another thing—if she leaves there may not be a space available when your dad figures out she can’t live at home. Some places have waiting lists.

I would let them do whatever they want to do. Especially at that age. I looked at it like from his stand-point and at that age any 'progress' is to small to compare with end of life requests. If she falls or God forbid worse, go into the weekends with the understanding that it doesnt matter 'where' death happens - his entire life is based on if he's "with" her until the end. Doesn't matter where - as long as they're together. Maybe they could be there at her location together for awhile?

See if he can stay at the facility with her in case things happen that they can take over

First, talk with the staff. Typically they advise that it is too soon to 'go back home' if even for a lunch. How about a picnic lunch somewhere? (bring the dishes from home as a reminder for her). How about a lovely drive?
Your Dad is the one who needs the most care. The love of his life is not with him on a daily basis. Of course he wants her back in an environment where he can pretend--if even or an afternoon-- that this are back the way they used to be.
It's hard to figure out who the 'patient' is at this moment.

It's fine to bring her home but you should still have someone else to supervise her within the home if you happen to not be in the same room as she is or something could go seriously wrong, etc. she could turn on the wrong burner or seriously burn something. It could be chaotic unless someone other than your dad is present. I wouldn't advise doing this unless you have someone else you trust to watch her.

I don't think that is a good idea, it will only make it harder to get her back to the MC facility and it might throw her routine off.....plus it will only make it harder for your dad to let her go back. IF you can now visit in the MC,,,,and if he can drive himself safely, he can go every day to see her, otherwise maybe you can take him several times a week to visit, then slowly back off the visits due to weather, etc. The constant change will only make her more agitated eventually. I wish you luck.