Payne working for the bomb squad makes a good deal of sense: it is clear he has some sociopathic tendencies, which while horrible in social situations, can be beneficial in periods of immense danger. Which would suit a man whose job is to defuse bombs.
Payne's hideout, a multi-story building in Pershing Square, not only gives him a view of the drop point and the surrounding buildings, but a high point to place receiving antennas for all his feeds without anyone noticing.
Payne's real drop, the subway electrical substation location underneath the trash can, gives him some lead time to grab the money and escape. The subway also gives him plenty of exits, enabling him to escape into the crowd had he detonated the second bomb vest.
Payne missed the dye pack because he didn't check the bag's contents. Payne did, however, have Annie empty the bag the money came in and put it in another bag. If there was a dye pack or tracker, he expected that they would be left behind. Only Annie either missed it or she knowingly transferred the dye pack into the bag to screw him. Since Jack was there, Howard was watching him instead of Annie, so she would've had the opportunity.
Payne choosing Los Angeles for his "jobs" benefit him two-fold. One, it's highly unlikely anyone in the city knows him. Second, the city is right on the water and close to the US/Mexico border. Had he tried to do the same jobs in his home city, he'd be at a disadvantage as he would easily be identified (or he'd have to take additional precautions) and he'd effectively be trapped in a land-locked city.
Payne having his police uniform and another bomb vest handy was part of the plan. He knew the police would be watching the drop. So he was always planning to detonate another bomb and kill some poor soul in order to escape. The only reason Annie was taken is because she was there, Payne recognized her and he knew she'd be the perfect hostage to keep Jack at bay.
