Hoods and bars at an angle
 

By accident (my stem bolts were lose) I have found it more comfortable with the hoods tilted back which also means the flat part of the drops is not level. Is this common or should they be straight? The downside is that when in the drops it's difficult to reach the levers and the down-shift button.

Depends who you ask. Now days you see road bikes with bars at all angles. Mine have a slight angle to them but not much. Probably best to adjust yours so your comfortable in both the hoods and drops.

Maybe you actually need a shorter stem so your reach isn't uncomfortable when the hoods are closer to where they should be.

That did occur to me. Does a shorter stem effect the handling of the bike?

Slightly

A shorter stem will make the bike more "twitchy"

I've found the shimano hoods to be more comfortable when rotated back a little bit. Two ways of acheiving this, though. You can either rotate the bars themselves, or move the hoods up a bit and leave the bars.

I recall reading that the design of modern shimano hoods is made to mimic the position you have int he front of the drops, with your hands in the curve, in which case it would make sense to have the "base" of the hoods about level. But whatever works. My drops are slanting slightly, but not a lot.

whatever feels good to you

i like the aesthetic appeal of having the "tops" and the bottoms both level to horizon... which also happens to be comfortable position for me