Looks like a clip that holds it has failed in some way. But for 'gluing'
it back down, RTV would probably be the safest thing to use. Although
that runs some risk as far as channeling water and of course holding it
down while it cures.

On the plus side, if you ever need to remove the trim in the future it
should be easy to cut the RTV and cleaning up any excess shouldn't be a
problem.

My best guess at it...

On that door trim...
If it isn't bent, the CORRECT way to repair it would be to get a roll of 3M
acrylic foam tape (try your local automotive paint supplier) It runs about
$22 a roll. Completely remove the trim and then remove all of the existing
two sided tape residue and then reapply the molding.
Here is a link to what the tape is, I just googled it, chose the first one,
you may find someone cheaper, I am just trying to show you the product.
http://www.levineautoparts.com/3mautgrayacp.html

To remove the trim, one of the guys in here says he uses heavy monofiliment
line and cuts the foam in the middle of the double sided tape with the
monofiliment.
To remove the adhesive you can use good old fashioned Ronsonol lighter fluid
OR  Paint thinner NOT lacquer thinner, but mineral spirits will soften the
goo and then you can roll it off with a terry cloth towel or your fingertip.
After you have removed all of the adhesive you should use a degreaser or
something like hot soapy water like Dawn or Simple Green to get any wax and
oils off of the area where you are reapplying and be sure that it is good
and dry beforeyou begin your repair.

Depending on how old your car is, you might try tugging gently on the
molding while drizzling lighter fluid down the area where it is pulling.
DON'T crimp it, pull at a slight angle but don't bend the molding very much,
no more than about 30-45 degrees. If you bend it too much you can put a kink
in it or crack the paint.

To run a straight line with the molding, you can stretch a masking tape line
above or below the moulding to use as a visual guide.
With the two sided tape, once you put it on, it should stay for years and
years. If it's REALLY hot outside, wait till morning or evening to apply it.
Don't be stingy with the tape. You'll be able to see where it was before, be
sure you reapply it as it was originally.

Man, I hope all of this helps, and I hope that you decide to do it right
rather than going the su'thn engineering route.

Kate