Vineyard we've only ever used German kindergartens and schools.
My eldest was a toddler when we moved, did 3 years of German Kindergarten and is about to start her 7th year of German school. When she started secondary (which was year 5) she had a classmate with an American mother for the first time, but the other girl won't speak English to her own mother let alone to DD, and they don't get on
they won't be in the same class together. DD speaks English to a girl on the school bus who goes to the next door school sometimes - German parents but brought up in Singapore til she was 8... but otherwise no English speaking contact at school.
English lessons are always a bit of a bone of contention because they are boring and sometimes the teachers get things wrong... However DS1 cannot spell in English so does benefit from English lessons purely because he has to learn lists of spellings - for some reason DD is a natural speller so I would have liked her to be able to choose a different first foreign language, so far she's learnt nothing in English lessons, but the automatic 1 (A) is useful to balance maths, which she sometimes struggles with

My older two sound like slightly posh northern English children when they talk (northern vowels, but no dialect or specific accent). Neither have problems with th or grammar. My youngest has the issues Bertie mentions though - which makes Ds1 cross, and he always corrects him
I can't make up my mind how much correcting to do.
I am fairly sure my youngest's English has more quirks because we tipped the balance too far in favour of German, mainly because I returned to work so he did far longer Kindergarten hours, but also because the house has become less a protected English bubble with two older siblings whose monolingual German friends are in and out all the time, and because my own German has got better! A parent who genuinely doesn't speak much German is probably the best way to ensure a child with perfect English!
Strangely I made less effort to socialise DC3 in German before he started Kindergarten and the older two used to simultaneously translate for him, so he had the strong English foundation as a definite first language, and his first language development was totally normal as a toddler, but I think we probably tipped him too far into German from age 3, with full 8 hour Kindergarten days instead of the 8:30-12:30 the older two did.
Bei used in place of 12 or more different English pronouns is my biggest bugbear, like Bertie - I hate it! Mind you when we visit my family I hear my nephew and niece (both of whom only speak English) using local dialect and slang and I think I'd hate being called "Mooomay" (I have now idea how to transcribe the pronunciation they seem to use) instead of Mummy more than I hate "bei" all over the place :o
- if you don't mix much with other English speakers you do get to control how your children speak English for far longer than if you live in your native country :o :o 