The installer in the op's photos sucks at electrical work, guys/gals, you know what a good connection feels like, this guy didn't check his work before stuffing the wires back into the box. He's probably one of those guys that says "You can't see it from my house".
Aside from that I'm a wire nut freak, I tend to over analyze my connections and I've come to have my favorite brands and techniques. If I'm lending a hand to one of my buddies, who buys the cheap tans, I think they're NSI, I only pretwist a little because the wire spring inside does not give to or conform to the splice so by time the nut is all snugged up the splice isn't wrapped up like king kong made it. (With these I could get away without pretwisting 14 but I just can't let myself do it) My fave brand is 3m models 312 and 512, these have more of a live spring inside and conforms nicely to the conductors, I'll pretwist to my liking with these. I still carry some Ideals with me though, the oranges are my go to nut when hanging fixtures, they're the best for one 14 and a fixture wire and their small blues are great for changing out ballasts. The original type in yellow (Not the winged one) comes in handy too as do the their tans, my former favorite.
Sorry now to get off topic but Peter D, you make me laugh bro. If I were still single you and I could fly over to Russia and meet some brides to be
I used to be in your shoes and know what it's like to want a respectable and intelligent lady but can't find one, it'll happen, you're a good guy. I met my girl at a friend's wedding, now our wedding is in Oct.