Beautiful looking '32. Some of the things you did that standout to me are the way you have the tinted windows, painted wire wheels, and I like the Flat Head. I'm also attracted to just about anything done in Orange.
One last thought. Say the molding isn't staying in place the way you want use a bit of tape to hold it in place until the glue sets up. I use Tamiya tape, but there are several good tapes in the market that would work just as well.
I cant believe what they pay for some items and think they're going to resell and make a profit. You know the old saying about one mans trash being another mans treasure.
I use a #11 blade to scrap the back side or use some sand paper. . You might want to place the trim face down on a micro fiber towel or some other surface that will not scratch the face of the molding. Go slow with real light pressure and you can press the molding against the towel and just sand a small section at a time. I usually put the glue in the grove so that you don't drop any on the body when you're installing the trim. You can also use some low tack tape to mask off the area around the grove if you're still afraid of glue getting out on the body.
You might try the glue you use for all of the rest of your kits assembly. Be sure to remove the chrome plating from the mounting surface if you haven't already. This is a case were less is more with the glue application for the chrome. I would also make sure before installing the chrome moldings that they will fit into the groves in the body. Sometimes to much paint buildup can cause a problem.
At that time the dish slot style wheels were very popular as you already know. I had a set of look a likes on my '67 El Camino that were from Shelby that were polished. As for your kit build Casey mentioned the S & H Ford and these may be the easiest to find but the AMT Studebaker Avanti kit also had a very nice set as well.
I have found in some cases that getting the glass in correctly so that it fits the opening is best done before adjusting for the interior. Sometimes the fold down sun shades will interfere with the windshield getting in place as well as the thickness of the area around the glass as well. Worst case if the glass is in as far as you can get it then sanding the bottom edge of the glass is needed or even the leading edge of the dash and interior. This shouldn't be by very much or there may be some fit issues else where.
The windshield looks like it isn't sitting all the way in the body and the rear window has the same look as well. there are mounting pins on the under side of the roof for the "glass" and maybe the glass isn't aligning as it should. I have had to enlarge the holes in the glass before to get them to fit, just a thought.
Hard to believe this is the same car. The paint is beautiful and with that shine you wouldn't be able to hide and body issues. The wide whites and full wheel covers look just right.