Check valve clearances first before doing compression test otherwise results aint to be entirely believed.

Normal glow/start-up time for primitive gorilla knob system is about 3-5 minutes, sounds like you aint glowin the plugs enough - hence crankin the engine way too soon. Yer first old-world diesel I presume? It aint nothin like modern diesels when it comes to startup ritual. Back in '73 these were not start and drive away cars but had to be warmed up. And primitive glow system is excruciatingly slow by modern standards. Thats 3-5 minutes just to glow the plugs you understand.

Meanwhile all diesels run rough to some degreee until warmed up, again check valve clearances and injector pop as referrenced below before worrying about rough cold performance. Otherwise you're outa yer mind tryin to diagnose engine condition of pistons, bores etc based on coldstart rough running. Start-up smoke/ unburnt fuel is also normal, though common culprit of incomplete combustion can be injector pump timing too.

My advice is change all filters, adjust valves and get injectors pop tested on yer newly purchased 220D. THEN decide how it runs after you're mastered the art of patience required in 3-5 minute glow/start and 10-15 minute warm up ritual. Otherwise weakness of the 220D is commonly worn out injector pump seals for never having it's separate oil sump monitored and oil changed. Worst case scenario there is $6-800 pump rebuild.

And rebuilt longblock (30k miles ago) oughta hopefully last another 70-90k miles if half-assed done correctly. Though personally am someone who believes old diesel shortblocks caint be properly rebuilt at all. Oughta opt for new factory shortblock instaed, says me. Question of pistons, rods and crank perfectly blueprinted and ballanced at factory that provides MB diesel longevity, procedure that rebuild shops caint replicate. I'd rather have an original decent running engine with say 250k miles than one thats been rebuilt.

Otherwise how's rest of the car? If its' got manual everything including sunroof plus excellent original paint then reconnoitre '73 220D to have immense long term classic value that shouldnt dip below $2500 USD with nowhere to go but up in value. 114/115's are hot ticket item right now, most of em doubled in value over the past 3 yrs. And question of massive upholstery, wing windows and pre-steelworkers strike German sheetmetal make pre-73/74 exceptional years for classic MB's better than 1974-'79.