"Student" wrote in message
When assembling the case, I realized that I wasn't able to fit in the
shelves into grooves on both sides, and align and clamp everything
together in time before the glue dries up.

Were these stopped dados (dados cut into a side but not running to any edge)
or were these straight through dados? What was to stop you from gluing two
shelves attaching both sides and squaring it up and clamping for the glue to
dry? Should be five minutes tops from start to clamping. Then you could
slide in the other shelves when convenient. Other alternatives are to clamp
square blocks at the 90° junction of a shelf and a side. A more exotic
method (and more expensive is to use something like these:
http://www.leevalley.com/wood/page.a...01&cat=1,43838

I also had a problem with the veneer chipping off the plywood for
every crosscut - miter saw, table saw, circ saw, all the same.

What kind of blade were you using? For cross cutting veneered plywood, I
always use a carbide 60 tooth combination blade at a minimum. Some things
that can help you with tearout is to use a zero clearance insert, score the
plywood on the cut line with a razor knife, or even have a thin sheet of
junk ply under the veneered sheet to prevent tearout.