Just to set the record straight:  this isn't a criticism of Tim's kit
or techniques.  I think the Apogee Saturn V is an absolutely beautiful
kit, I'm thrilled with it, and if I had the money I'd buy a dozen.  My
building skills are rather limited; I've never built a kit as
intricate as the Saturn V before.  It's my hope that this post will
help someone else that's been having similar problems.

The gluing of the wraps is the part of construction that scared me the
most.  Tim shows a construction technique using fast CA (thin). 
Someone else on RMR suggested practice, so I practiced the technique a
number of times using scraps from the the wraps.  Now, some of the
edge scraps are extremely thin and aren't going to glue down properly,
so that a bad result on the scrap won't necessarily mean a bad result
on the real thing.

BUT... I simply couldn't get the technique to work properly.  Thin CA
is a good solvent for polystyrene, and even the thicker scraps would
dissolve and crack. (I think this is more of a comment on my lack-of
building skills than on anything else; I've never built a rocket this
intricate before, and I've never used CA to build a rocket before.)

An alternative technique, which was very successful in my hands, uses
medium CA instead of thin.  [Warning:  the CA I used was several
months old, which may have something to do with the properties of the
stuff.  Anyone who wants to try this technique would be well advised
to practice with scraps on a piece of body tube first.]

I found that the medium CA didn't dissolve the plastic of the wraps
anything like the thin CA did.  I could actually run a bead of medium
CA and let it cure without the plastic dissolving at all.  If you find
that your medium CA dissolves the plastic too, it may be too fresh...

My technique was much the same as in the video, except that I
carefully stretched and taped the wraps into place, and made sure that
they were just where I wanted them and as tight as I wanted them,
before gluing.  Then I simply ran a bead of medium CA on the edges of
the wraps, using a very fine tip on the CA container, and let it cure.

Using this technique, the thrust structure wrap (bottom) is actually
more difficult to do than some of the others.  I did glue it down
first, but to get the proper feel and practice, it might be better to
glue the intertank wrap first.  The intertank wrap (just above the
thrust structure) is a nice simple rectangle with no projections.

My cutting technique on the wraps was less than perfect, so the top
edge of the intertank wrap snugged up nicely to the tube, while the
bottom edge gapped away from the tube just a little, maybe half a
millimeter.  I found I could stretch the wrap so both edges would
touch the tube -- but that left a misalignment at the seam.

My solution was to ignore the gap at first, glue the "snug" edge down,
then glue the "gapped" edge down a couple inches at a time.  After
applying the medium CA to the gapped edge, the bottom edge was pressed
to the tube and held there for two minutes (that's how long it took
for the glue to grab really well).

When doing the thrust structure, the places between the four fairings
were glued down first, just as Tim suggests.  When that glue was
completely dry, the fairings were done by applying a drop of medium CA
to each corner, and holding down the corners against the tube until
the glue set.  Then a bead of medium CA was run along each edge.

Here lies a problem with this technique.  Medium CA is slower than
thin CA, and polystyrene doesn't glue all that well to the paper tube
anyway.  That means that this method is significantly more
time-consuming.  In some places like the fairings, you have to do a
little at a time, hold the pieces together for two minutes, then do a
little more.

Another problem that I've already alluded to is the fact that for the
most part, the wraps have to be very carefully taped into place and
ready-to-go before you start gluing, because the medium CA takes so
long to set.

I finished all the main body tube wraps in two days, except for the
sticky-outy parts on the interstage wrap.  Each sticky-outy part will
have to be glued one at a time.  That's going to take a good while. 
But hey.  If'n I was in a hurry, I'd'a done it weeks ago.

Regardless of the technique used to glue the wraps, some practice with
the scraps from the wraps will pay off handsomely.

Last comment for chemistry geeks:  you probably know this already but
if you can get 10-100 microliter plastic pipetter tips, they work
quite well as extension tips for the CA bottle, and they're so doggone
cheap that they can be thrown away after one use.

Hope this helps someone,
P'rfesser