You can check the accumulator by connecting a pressure guage to the fuel line -- the accumulator should hold some pressure in the system nearly indefnitely. Before you replace it, check the pressure drop on the fuel distributor and feedback frequency valve, because failures here will bleed all the fuel pressure down rather than holding at system pressure.
You can test the vacuum modulator with a MitiVac pump. Check rubber connectors on plastic lines before replacing -- which leads me to ask, are you having late, hard shift problems with the tranny? If so, look for the vacuum leaks!
Usualy failure mode on the fuel distrubutor is to go way rich and stay there from incorrect differential pressure inside. Not fixable by the DIYer (or the MB shop, for that matter!). Can only be tested with the proper equipment.
Get the fuel flow tested before replacing, it costs $1200 or so! Lean on a few cylinders can be a vacuum leak rather than bad fuel distributor, and will give hard starts due to no fuel (the air isn't going through the venturi).
Things to check are vacuum line to brake booster, brake booster itself, vacuum supply line for locks and climate control, and intake manifold gasket. I don't know if the fuel distributor/manifold is a two piece setup like the D-Jetronic or not, but if it is, there is another leak potential. The idle control valve hoses will get hard and loose with age, too, causing intermittant vacuum leaks and unstable idle mixture. If the mixture is adjusted while they leak, the problem gets worse. Check and replace, then adjust idle mixture without the leak. I ended up replacing all the vacuum line rubber connectors on the 88 TE to get a rough idle fixed -- still not done, I suspect the OVP relay and I've still not adjusted the mixture correctly. You can also get al leak at the pressure transducer in the computer (on the fender, small vacuum line from manifold to sensor) -- a leak here will cause mixture control problems.
A vacuum leak will also cause the mixture feedback circuit to mis-behave, since it measures residual oxygen -- excess air going into part of the manifold will cause the feedback circuit to assume the engine is running lean and add more fuel. This will eventually foul the plugs on the cylinders not affected by the leak, causing misfires and hard starts.
And don't forget the cold start valve, either -- if it leaks and dribbles fuel, it also doesn't spray properly. Bad spray will cause cold start problems, and leaks will cause rich running, excess fuel consumption, and flooding on hot starts! On the M103 it goes in the idle valve hose, so replacing the hose may fix some of the problems, too.
And last, what condition is the ignition in? Old tired, burned up cap and rotor, dead plugs, and leaking spark plug cables will cause all of your problems!
1972 220D ?? miles
1988 300E 200,012
1987 300D Turbo killed 9/25/07, 275,000 miles
1985 Volvo 740 GLE Turobodiesel 218,000
1972 280 SE 4.5 165, 000 - It runs!