Without feeling the paint, it looks like Hard water spots combined with a cleaner stain, (and at spot where it looks like something abrasive was rubbed in a circle). Seen worse get corrected by the following:
Step 1. Clay bar
Step 2. Compound
Step 3. Polish
Step 4. Wax
I used Meguiars products because you can get them at Walmart, AutoZone. ETC. and they are priced very good. I also have a Dual Action (DA) polisher because my shoulders are over 50. You can use an orbital but it is safer with a DA since it will not burn your paint during the correction process if to much pressure is used. There are a lot of videos out there on how to step through the process (Meguiars, Mothers, and Turtle wax have some good ones posted on there site).
I am not pushing Meguiars, but I have had great results with their products. You can shop around, and pay a lot more for something like Chemical Guys, Adams and what not but have never found there products to be any better really.
Do a test spot first, and if you decide to do the paint correction, the biggest thing ot remember is to work in small sections (2ft x 2 ft) at a time as each Step is applied.
PS EDIT Before Step 1 wash the Jeep first with some Dawn.