I have 2 of these, one in the man cave and one in between the living room and the kitchen (open plan). Overall I'm really impressed but they do have their annoyances.
Harmony integration - I have shortcuts set up so I just say "turn on plex", "turn on sky" etc. The harmony will respond immediately turning on the connected equipment but google home insists on telling me "OK, getting harmony", Harmony will then respond "Turning on plex". This means it tells me it's getting harmony about 5 seconds after the command has run.
Not being able to share timers across the 2 home minis. - I want to set a timer in my kitchen and get the notification on the one in the man cave. I burn food a lot!
"Hey google/OK Google" - It's a bit of a mouthful especially after a few cans, I much prefer the amazon wake words. Alexa rolls off the tongue much better.
"youtube music is not available in your country" - If I want to play a youtube video on my chromecast I have to be very specific with the video name otherwise it thinks it's a song name. For example I watch James Bruton videos on youtube, if I say "Play james bruton on youtube" it thinks he's a music artist and gives me the youtube music error.
The LEDs - when I first turned it on the LEDs were the google colours. Ever since then they've been white unless I turn the mic off.
The control buttons. - The one in the man cave is wall mounted. There is no official way of swapping the orientation of the vol up/down buttons. I have run my cable out of the top of the device and along the edge of a windowsill to get around this issue. This function is available in the unofficial API which shows it has the ability to, google haven't made that feature available in the app yet. https://rithvikvibhu.github.io/GHLocalApi/
"The mic's off" - Thanks, I know that as I just flicked the switch and the leds have gone orange.
The shopping list - add things to your shopping list and you need to be online to retrieve it. Great, but I don't get a signal at my local Tesco making this feature useless. Why it doesn't sync with an offline shopping list on your phone is a mystery to me.
Blocking offensive words - I'm an adult, I swear a lot and have this turned off in my google assistant preferences. I can get my phone to tell me to fuck off by saying "vaffanculo", google home beeps the word fuck. On a plus note you can swear at it, I created a duplicate room for the man cave called "fucking". Now I can say "turn the fucking lights on". It's just a shame it responds with "sure, turning 10 lights on" instead of "turning on the fucking lights".
Lack of plex integration. - This is more of a wish than an annoyance. It would be nice to be truly lazy.