Heh, I've had the opposite experience. Generally sites that completely ignore mobile are manageable on the phone, maybe I have to scroll around a bit but its not a big deal. Mobile specific sites however seem to "break" (or at least annoy me) spectacularly and frequently.
If I press the menu and your menu takes over the entire screen, seemingly like a new page, the back button should close the menu, not navigate off your site, especially if there's no way to close the menu other than navigating to a link. Floating elements that take up 20% of an already small screen with absolutely nothing useful on them and no way to get rid of them are broken. Redirecting a non-mobile link to the home page of your mobile site instead of to the content the link actually points to is pretty common too.
In general I HATE mobile sites because they're usually less useful than the real desktop site or break things like reader mode. I'm especially FOND of sites that try to implement their own gestures thus messing up scrolling or the system gestures. That means YOU imgur.
But I've never seen an app present me with the equivalent of 3pt text by default.
Blogger is the worst example. I'm basically unable to scroll an article without it interpreting it as a swipe, sending me to a different page, and losing my progress.
If I press the menu and your menu takes over the entire screen, seemingly like a new page, the back button should close the menu, not navigate off your site, especially if there's no way to close the menu other than navigating to a link. Floating elements that take up 20% of an already small screen with absolutely nothing useful on them and no way to get rid of them are broken. Redirecting a non-mobile link to the home page of your mobile site instead of to the content the link actually points to is pretty common too.