I'm not sure, but you may have just coined a new word: "Lumpily." I like it!
OK. Let's get down to business:
First of all, is this a new car? (To you, anyway?) Or have you owned it for a while and these symptoms have developed recently? I must ask, because my '87 Mercedes turbodiesel is as healthy as a horse but she runs like a crippled mule for several seconds after startup. And that's in the middle of the summer during a heat wave! (I can't wait to see what winter is like.) If you just purchased the vehicle its certainly possible that this is normal behaviour. (Notice how I threw that superfluous "u" in there so you'd feel at home.)
If these symptoms have developed recently then the list of possible culprits is mercifully short. You can eliminate "ignition" or "mixture" problems right away since they are irrelavent to diesel engines. That leaves only glow plugs, air intake, fuel injection and exhaust.
If the engine fires immediately when cold, but then idles poorly, I would imagine that the glow plugs are probably working correctly. Otherwise the motor would require a lot of cranking to start. One or two bad glow plugs could cause the symptoms you've described, though. It's simple to test the glow plugs using a multimeter. Unfortunately, I don't know how.
But give 'em a few minutes. Sooty, Brodie or Christi will chime in soon. They'll know how to do it. (So would any number of people over HERE, too, but most are smart enough to go to bed when they get tired. I'm staying up eating a microwave turkey pot pie and talking to YOU instead.) Just because the plugs were recently replaced doesn't mean one or more aren't faulty. The fact that they're new means they'd be the FIRST things I'd check! Any time you change something, and another problem suddenly appears, there's a strong chance that it's not coincidental.
If the glow plug system, including the relay, checks out then the next question is: How does the motor run once it gets over its initial shimmy 'n shake routine? If it runs strong, and idles smoothly (for a diesel) then serious internal mechanical problems are unlikely. Bad compression in a couple of cylinders wouldn't go away...the poor idle would continue. And it would almost certainly be accompanied by excessive oil consumption as it leaks past the worn rings or valve guides.
If it's not glow plugs and it's not an internal mechanical problem, then it must be a fuel injection issue. (Clogged intake or exhaust would cause severe lack of power, and probably a lot of black smoke, but not the symptoms you described.) Again, the fact that the injectors were recently changed might be a clue. One of them might be faulty. But this isn't a strong possibility, because a bad injector would remain "bad" once the engine is warmed up. One thing to consider, though, is that one of the injectors (or the fuel circuit leading to it) might be bleeding off pressure after the car is shut down. It might take a few seconds for it to "clear" and begin working properly when you start the car. I know this can happen to some Mercedes gasoline injectors.
If I had to venture a guess I'd say that the glow plug system has a fault somewhere. I'm led to that guess by the fact that the problem seems to cure itself after about a minute of stumbling and shaking. A cold diesel engine, without glow plug assistance, is a very cranky beast. The fuel doesn't want to ignite, and when it DOES it tends to explode violently. And because the individual cylinders will warm at different rates the result is a very unbalanced and unhappy idle. (Does it smooth out a lot if you rev the engine during the "stumbling" period? And does revving the engine for a few seconds seem to shorten the duration of the "stumbling"? If so, that would also point to glow plugs because revving the engine means more rapid compression of the intake air and hence higher temperatures at the moment when the fuel is injected.)
-mickey