Not sure what you can say about a post office... I needed to mail a package on a Saturday, and looked up "post offices" on Yelp after taking a grad school exam. The directions were good and I found the place with no problem. This location, however, isn't open on Saturdays (the window). If you want to mail anything on Saturdays, you'll have to use the Automated Postal Center (APC) machine.
This location is open only Monday through Friday. I don't live in Mesa, but judging from all the locals coming in asking what was wrong, I take it they're not used to this either. I stood in line a long time behind this lady who was mailing a litany of large envelopes...long enough to tell several people to read the hours posted on the outside doors.
The post office is beside the Mesa airfield, and looks fairly new. I didn't have any issues other than expecting to be in/out and that wasn't the case. There's only one APC that I saw, so if there's one person with an armful of packages to mail, bring a book.