Obviously I am 99.99% sure I am clicking correctly, yet Recaptcha displays me another and another captcha, until it lets me move on. Is it a system bug or maybe their bot detection got quite unreliable?

Neither. When Google finds someone willing to train its AI for free, it likes to take advantage.

You are a bit sarcastic. What can a user do? Either he continues solving "train their AI for free" until the let you move on or you leave the site?

You can complain to the site operator. Google is not forcing their captcha on websites. If enough people do that, perhaps site operator(s) will take notice. Tell them exactly what you don't like so they don't eventually change to different vendor, but same annoying captcha tech.

I remember one particular set of pictures with both buses and coaches (and some with neither) on it, and it asked me to click on the buses. It said I'd got it wrong, but presented an almost identical set afterwards, and I included the coaches, but that was also wrong.

I've seen this happen, and I think it was because the IP address was previously used for craping of some sort, or somehow set off some flags at Google. VPN providers can cause this because sometimes their IPs are used for just such things.

It doesn't seem to matter which images I click, it lets me in after a while anyway.