Phosphates
This could be an issue with your vintage machine. Phosphates were removed from dishwasher detergents across the board about two years ago or so, and spotting, filming, and generally poor cleaning results ensued across the country. You can find institutional detergents that still have phosphates, but you'll have to look for such products somewhere besides the supermarket. Your previous dishwasher could manage without phosphates because it ran so damned long. Older machines were designed to get the job done quickly, but also presumed the detergent would contain phosphates.
If your water is soft enough, you may get away with phosphate-free detergent. I've read here that people are having good luck with the "power ball" and packet/tablet types of detergents, but take a good look at them to make sure they'll fit in your dispenser. Also, using a product like "Lemishine" (basically citric acid and available at Target) will help. I'd recommend running a full cycle with Lemishine (with dishwasher empty) to clean the interior and other components before putting the machine into regular use. But first, with tub door open flat -- and you won't be able to see it unless you stick your head inside the tub but you can just feel around with your fingers -- all along the bottom of the door there's a lip where funky greasy residue tends to accumulate. Clean that stuff up and keep tabs on it going forward.
Any items with caked-on soil should be placed on the bottom rack tilted toward the center of the tub to give the 4-way Hydrosweep spray arm the best chance at getting them clean.