or Pine trees, palm trees (especially of the Pindo variety...pretty sure the squirrels are tossing the seed shells into the pool while I sleep) or pretty much anything else.

Not sure how creative you want to get or how much you are looking to spend on this issue or for that matter how much space you have to work with - but take a look settling tanks used in garden ponds (for Koi and the like). The leaves are more of a problem there since you generally have a lot of vegetation planted right on top of your pond, and since you don't have the chlorine, when they start to break down they can fowl the water pretty fast...so you want to get them out as easily as possible.

The tank I used with our old pond (had honey locust leaves which posed a similar issue as your mesquite tree) was pretty simple. I took 1/2" acrylic and cut it to my needed sizes. Built a tank with the inlet on one side (PVC) and the outlet on the otherside (also PVC). In the middle of the tank I had three walls which went from side to side. The first one went from the very top to about 2 inches above the bottom of the tank. The second wall was from the bottom to about two inches below the water line. The third went from top to bottom but was made of a perforated acrylic sheet (looked a bit like peg board with a bunch of 1/4" holes drilled in it). It was made with two sheets separated by about 1". This allowed me to slide a piece of fiber filter material in between the two panels to catch any big stuff still in the water column - almost like the cheap A/C filters. The overall size of the tank was about the same size as a 55 gallon aquarium (48" x 16" x 24" or around there. Everything was solvent welded with acrylic cement. As the water came in from the inlet anything that would float would float up to the top before the first wall. Since the velocity dropped so much (going from a round 2" PVC pipe to a big open chamber with a space 2" x 16" for the water to flow through), anything that was a sinker would sink as the water went over the second wall. When it got to the fiber filter, about all that was left was bits of soft organic matter that had the same density as water (or close to it). Once a week or so during the fall I would open the top and scoop the leaves off the floating side, suck the junk out of the bottom and rinse off the filter. Previously I had to deal with the proper filter clogging up about every three days.

You would obviously want something that is different then that to some extent in that yours will likely not be able to use normal siphon actions to keep the flow going (the water line in my settling tank was the same as the water line in the pond). However, I know that there are commercially available units which do the same thing and are sealed systems (look a bit like a small sand filter IIRC). Take a look around and you might be able to find one that you can plump into your system to take care of the problem.