In pretty much every stream/video I've seen, the police radio image and the various windows drawn by other plugins (Traffic Policer's observation window, Arrest Manager's prompts to take suspects in yourself, the assault callout's descriptions of the victim, etc etc) show up fine... but for some odd reason I can almost never get them to show when I'm streaming or recording. I'm using OBS to record with Game Capture, and I think I've seen them show up twice only. The fact that they've shown up twice is even more confusing, as there is literally nothing I've done differently these two times (once, I was recording without the windows showing and GTA crashed... relaunched GTA and restarted the recording, and police radio etc showed up fine.... GTA crashed again a bit later, restarted both, and it was gone again!)

Has anyone had success with getting police radio etc to consistently show when using OBS/Game Capture, and can maybe offer some tips on what I can tweak to get it to show for me?

I have the same problem, I believe since Police Radio uses outside images it does not capture. Try using 'Screen' or 'Monitor' capture instead of Game.

The way the texture drawing works, it may not show up in OBS's game capture due to DirectX issues.

As bacon said, try 'screen capture' or 'monitor capture'. Setting your game to borderless may help too.

It has to do with the program you use to record... I use the recorder that comes with Razer GameBooster (freeware). It's great quality, free to use, no adds or watermark(except if you tab out) and it records the entire screen, addons, popups and all.