Find the threads about how to desmog. They might be in the FAQ sticky post at the top of the 60 section. It's too hard to parse out what may or may not be wrong from a couple photos, but that guide will help you eliminate some possibilities.
Right away I can tell you the black & white vacuum valve clipped to the underside of the air cleaner, above the dizzy, is bad. In several years of testing every one I can get my hands on they've all been bad. There's a black & blue replacement from the 80 Series that works for that, it's an active Toyota part number but you can find it on City Racer's website too. That vents your dizzy. If the dizzy doesn't vent it can corrode inside. The line that tees off just above the PCV valve and connects via hose to another valve way underneath the air cleaner can probably go. Just remove the tee and run a hose straight from the PCV valve.
The caps on the top of the carb that are cracked won't effect vacuum but replace 'em anywhay to keep crud out. The big port in the air cleaner with tape over it won't hurt anything like that.
Use
@MoaByte's suggestion above, or if you're feeling lively use carb cleaner and spray around until the idle goes up - found your leak. It may only go up just barely.
Check the nuts that hold the carb down, retorque the intake & exhaust manifold bolts (I think 33ft-lb, but please double check; and yes you can get to all of them without removing anything else in the engine), make sure the caps on the triple nipple thing screwed into the intake manifold are good (Toyota calls that a "gas filter"). After that and the soap or carb cleaner spray, get the Emissions Factory Service Manual and start testing the vacuum valves that you still have.
