John is right that I’m not having problems with SketchUp 18.1.1180 under Mojave 10.14.2.
However, I can’t say that installation of Mojave itself was without issues. For impatient readers, I’ll cut to the chase: I think Mojave is more sensitive than past macOS installations to detritus left behind by previous macOS versions. A disk wipe and clean install may be the only way to get it working on some computers.
Now the details of my specific case. When I first attempted to install Mojave, the process took a very long time - like 4-5 hours, not the 35-40 minutes Apple says is normal. When I fired up the computer at the end of the install, everything was glacially slow. Simply typing my password to log in required 15-20 seconds before each character responded! Opening Finder took several minutes! The system proclaimed it couldn’t connect to my WiFi because there was no adapter hardware detected. Fortunately, I keep good backups, including an externally bootable carbon copy, and I was able to restore High Sierra without difficulty.
A bit later, I took the Mac to the Apple store for a battery replacement (it is a 6-year old MacBook Pro with a lot of charge cycles on it). They had a local copy of the installer and agreed to try it for me. The installation itself went faster, but with the same end result. The “Genius” there had no clue of what was wrong. His only suggestion was to erase the disk and do a clean install, which I rejected because I really can’t go without the computer for the two or three days it would probably take me to re-install all my apps and data, including licenses.
Then I went online and searched for reports of similar issues. Lo and behold, I found hundreds of people reporting exactly the symptoms I was getting. And one person had tracked it to an obscure system configuration file that evidently Mojave doesn’t erase or overwrite during installation. The advice was to delete that file, as it is a tweak not an essential anyway and then retry the installation. I did so and presto! Mojave went in cleanly and has been fine ever since! And here’s the really strange part: shortly afterward, Apple deleted the discussion topic where I saw that advice from its forum! No explanation, just poof!