It depends on what kind of American. When I was in London, I didn't particularly enjoy myself, I didn't find much entertaining, nothing seemed that authentic, there wasn't really a middle ground between touristy cheese and business. But I was also traveling with my slightly kooky grandfather, who wakes up in the morning thinking it's still the 70s, so that might have had something to do with it. If I lived in the UK for any period of time, I'm sure I'd have a lot more to complain about.
If I were to think of some complaints Americans would have regardless of age, political leaning and geographic origin:
-Difference in nomenclature
-Some accents don't even sound they're speaking English (e.g. Geordie)
-Cars and gasoline are more expensive and fewer citizens own them. Americans outside of urban areas don't really use all that much public transportation.
-Prices on goods and property/rent are much higher than most of the US.
-People in courts wear silly wigs.
-Overly-lenient courts that favor the perpetrator.
-Laws like ASBOs or prohibiting the sale of tableware to minors.
-Those silly guys wearing head to toe Burberry standing outside an unemployment line.
-That despite how much flak Americans get about their beer, food and weight, Brits drink as much crap (Carlsberg, Stella, Carling Black Label) eat as much if not the same crap and are rapidly approaching similar rates of obesity.
-Inside smoking bans, although most of America is the same way now.
-A lot of unflattering architecture. Dilapidated ancient buildings or dilapidated "modern" high rise tower block eyesores.
-This:
Food should not be neon colored. Food should not contain both sugar and artificial sweetener in it.