I have a 3/4 hp model. No problem with anything except I wouldn't put
a whole corn cob through there (husks are probably okay, though I
usually scoop them up and throw them in the trash).

I've found that when I cut a lot of meat and toss the scraps (could be
a pound or two of scraps) into the disposal, the meat goes through okay
but when I stick my hand into the drain the fat is still sitting there.
Too bad it isn't the other way around-- I could use the disposal to
get rid of the fat and keep the meat!

So, when I'm done with making burgers, I scoop out the gobs of fat and
throw the mess into the trash. It's still a nicer deal than cleaning
the sink.

So far nothing has broken the unit in four years, so I'm willing to see
what works...