First of all, let me say that the still doesn't quite give justice to the awfulness of that matte shot. The foreground component had much too low contrast, and stuck out like a sore thumb. Fortunately, I haven't yet seen an effect that bad in the show.
You're right in that it's old, but that's not the problem. Remember that the film Fantastic Voyage was made two years prior to this TV show. And the visual effects for both that film and this show were handled by L.B. Abbot, Art Cruickshank and Emil Kosa, Jr. All of them were very competent visual effects men.
But you are right about budget restrictions. I'm sure that's the main hurdle. Still, the show looks quite good. Not as good as today's CGI effects, of course, but still quite good. And these old school effects have something that CGI effects usually lack; a certain kind of presence.
Most of the small/big shots seem to be done with split screen, although the split is unusually hard to spot. Some shots may have been back projection, but you can usually spot those because the background has more grain and/or less contrast than the foreground.
No, if I have any problems with the show it's not in the effects department. The premise of the show - the giants are out to get us - doesn't really lend itself to a very great variety of stories, so it's not a how that I enjoy binge watching. An episode now and then works fine, though. But the thing that really bugs me is that the Fitzhugh character (played by Kurt Kasznar) is so annoyingly one-dimensional.
51 episodes are going to last quite some time for me, I think, but as long as I pace them a bit I think I shall enjoy them.