Best would be to post screenshots so that we can find out what the issue is.

https://www.flickr.com/photos/jd430w/35618162134/in/dateposted-public/
Should I post the offending model to the library as well? I was saving it for when I had it posted on LEGO Ideas.

Can you give us the reference of the part that is the trouble?
Can you post a screenshot of the workshop under the same POV as the one of the render?
Having the model would definitely help.

http://mecabricks.com/en/models/DoK2w5B6v9k
I decided just to post the model, it'll be easier for both of us. There are probably about 200 parts affected, but ONLY the windows and windshields, which is bizarre.

It works fine with me. Now that it is an add-on, a good part of the video is obsolete. Did you make sure that you use "Import > Mecabricks (.dae)" instead of "Import > Collada (.dae)"?
On you render it looks like that the materials have not been replaced.

Ah, I used the Collada option; I didn't see the Mecabricks option. I didn't think that much would have changed. I'll try it again and see if that works. Is there a newer official tutorial I can watch anywhere?

Open the PDF file which is in the folder and see the last step. Nothing else to do after import. You are ready to render 😉

New problem: I don't get the Mecabricks .dae option in the Import list.

This is because you did not install the addon.
You need to download the lastest file from Mecabricks and then follow the instructions in the PDF file attached.

Okay, but now some models don't show up at all. My Washington DC Skyline turned out beautifully, but the Monorail Cab doesn't show up at all in Import>Mecabricks, but it does with Import>Collada but with the wrong colors like before, as does the Monorail Full we were testing on. I suspected that perhaps there were too many parts, so I tried a smaller model of mine and only one part appeared in Import>Mecabricks (a boat slider if you were curious; I know I would be) but using Import>Collada it worked perfectly.

Maybe it's groups. The two monorail ones I tried had groups and the Enterprise I just did (the one with the boat slider) did not. Of course, the DC one also had groups, so that probably rules that out. Just a thought anyway.

Don't try to look too far. The add-on works with groups, no groups, a lot of parts, etc. Forget about the collada importer.
There is something that you might not do correctly or not the same every time at least. You simply need to figure out what.
To make sure, start fresh with newly exported models from Mecabricks.
I don't rule out the possibility of a bug somewhere but it looks pretty unlikely according to your issue.

Which version of Blender are you using?

Again for us to help you, you need to give the link of the model that you try and that doesn't work, then explain in details the actions you do. It has to be repeatable. Otherwise we won't be able to do much.

Renderbricks pointed out to me that I might be doing things in the wrong order, so I'll try that.

Okay, that didn't help, so here goes:
Blender 2.78

1. Mecabricks- File>Export>Collada, Group by Geography, Normals:None, LEGO logo on studs
   Save file to desktop
2. Blender: Open Blender
   File>Open>Lite 1.8.9.blend
   Select bricks and delete
3. World>Environment Texture>Open>random studio HDRI pack
4. File>Import>Mecabricks>[file]
   So here is the problem. After this step, the monorail I shared with you does not appear. It and it's parts show up in the side bar with Scene, Renderlayers, camera, ground, etc. in it, but in the two panes where you can manipulate the model and camera it does not show up. It gives me a point that I can move around and scale like usual, but the model itself is invisible. But other models do other things:
   In this model one macaroni tile appears and that's it: http://mecabricks.com/en/library/search?q=uss+discovery (USS Discovery)
   This model worked fine: http://mecabricks.com/en/models/WPkaJBd8axM (Washington DC)
   This model does not appear either: http://mecabricks.com/en/workshop/r0DvY6kZa9e (Park Ranger Brickheadz)
   Trying them with the Collada option even though you said not to produces different results. The USS Discovery showed up mostly white with a few bronze pieces and the Brickheadz appeared as it was supposed to. The DC Skyline does not appear using the Mecabricks import option but appears correctly using the Collada option except for the decorated elements, which come out white.
   I hope this is enough information for you.

You shall not use file "Lite 1.8.9.blend". This is a recipe for disaster as this file is post add-on and contains incorrect data.
Add-on can import a Mecabricks model in any Blender scenes. Therefore, you shall either use the default startup scene or the file called 'Template.blend' that you will find in the add-on package.

1. Install add-on 2.0.5 as per PDF File.
2. Open file 'Template.blend'.
3. File > Import > Mecabricks (.dae) > {your file}
4. Choose a HDR Image and set up the camera
5. Render

Here is what you shall get after step 3:

This seems to have fixed everything! Thanks for all your help and patience. I'll let you know if I discover any other problems. (Just what you wanted to hear, I'm sure...)

How do you render printed pieces?

You don't have anything to do. This is done automatically during import.

The decorations weren't showing up in the viewer but I didn't check the rendering preview, which they do show up in. Oops.