I’m currently running iOS 15.6.1 on my iPhone, and very curious about the new features of iOS 16. However, I’m always a bit leery of updating to any new OS, too soon. I generally like to wait at least until a dot (16.1, in this instance) update has been released. That being said, have you all had any issues with v16? Any gotchas? Any, “man, I wish I’d waited …”? 
Cheers
Honestly, none at all for me. Some people are having issues with battery drain compared with iOS 15, but I am not - my battery remains the same, if not better. That would be my one caution to anyone who is reluctant.
Also, rumors are that there will be some sort of Apple event this month to introduce new iPad updates and Mac updates (as well as iPad OS 16.1 and MacOS Ventura), and the 16.1 beta sounds as if it is working pretty well (I never run betas myself, but from what I have read), so I am thinking that 16.1 is not very far away at all. If you’ve waited this long, perhaps wait to see what 16.1 brings (and it is rumored to add the shared libraries feature for iCloud Photos, so maybe waiting to see if 16.1.1 fixes any bugs in that feature?)
Updated my 2nd gen iPhone SE to iOS 16. No issues to date.
Some interesting new features. I inadvertently invoked iOS 16’s ability to eliminate backgrounds on a picture I sent over Messages. Had to double-take to figure out “How the heck did I do that?”
No problems here, and I’m running 16.0.2.
Apple Discussions has several reports about Homekit Automations being broken with iOS16. I am holding off until this is resolved.
Just a quick reply to that - all of my HomeKit automatons are running just fine, in two houses. (Anecdotal, of course, but they all run fine.) I don’t have any that are when people arrive / when people leave, but there are some complex ones that kick off when humidity levels rise and fall (for a dehumidifier) and when temps rise and fall.
Also, is that more a tvOS / homepodOS (is that what they call it?) or an iOS issue? Automations (it seems to me) are run on the HomeKit hub, which are either an Apple TV, a HomePod, or, for now, an iPad (but iPads are still on 15.x).
Thanks Doug. My AppleTV and Homepods have automatically upgraded to version 16. My automations (mostly time of day based) seem to be OK except a recently created one. Yesterday I deleted it and recreated it with a different “on” time (*) so I am waiting to see if it works today.
Many of the apps I use in Carplay is broken in iOS 16. Podcasts app (stock), Audible and TomTom nav just to name a few all freeze up for me.
Audible works fine for me in Carplay. I thought iOS 16 was the most painless upgrade in years. Though saying that, I have probably jinxed myself!
I Should have waited a few more days for 16.0.3:
See also my description of issues upgrading from 15.6.1 to 16.0.2 with our family iPhones (update from iPhones Settings only gave me the option to install 15.7, which failed):
Installed 16.0.3 last night. I hope that will fix the issues. I also deleted my Carplay and Bluetooth connection between the car and phone, if this doesn’t fix it I have a service coming up for the car - perhaps they have a software update for the car (Mazda CX-30 - 2020)
Still had issues after removing carplay/bluetooth profiles both in car and on phone 
I think I found out what caused the problem on my phone (13 pro). It was the TomTom navigation app - I uninstalled the app and the issues disappeared. Somehow that app “stole” almost all the “attention” in Carplay.
I waited for the iOS 16.0.3 and all is well, except I am enjoying (NOT) a battery drain. Having to charge my iPhone during the day is annoying. I guess I’ll go back to turning everything off that I find useful. 
See this discussion from last year:
“Settings / App Store / Video Autoplay Off seems to have fixed it…” and the next item about temporary high battery drain after updates.