From description of the issue I would defer to @Paulster commentary.
This sounds like a traditional lean condition caused by a vacuum leak. Vacuum leaks typically reveal themselves under low RPM conditions due to how extreme the lean condition can be at idle. As the rev's increase the engine still has a lean condition but is overcome by the additional fuel to find a better balance and is able run in what appears to be a smoother fashion.
Additionally, when the AFR (Air Fuel Ratio) comes close to to 14:1 the lean condition can translate to more power due to the additional oxygen that is being provided. The dangerous long term risk to the motor is that it will run much hotter and can even run hot enough to destroy your exhaust valves as the overheated exhaust gasses are passing across exhaust valve face and stem and not the intake valves.
You can troubleshoot the condition using a technique used frequently by motorcycle mechanics but beware what I am offering as a potential troubleshooting technique can be potentially dangerous.
I use contact cleaner that, if burned, has a emission of NOx (Nitrogen Oxide). This is different from Nitrous Oxide, which is to charge whip cream cans among other things. Contact cleaner is used in many cases to clean electrical contacts and has a very low oil residue within it. Unlike gasoline or brake clean, if it ignites it burns off very quickly due to it's high combustion rate.
You run your engine and use the little red tube that comes with the can to spray small amounts of the contact cleaner onto areas of the FI or carb you suspect may have an air leak. More than likely there is a vacuum line that was not put back in place and you might find the nipple for the vacuum line on or near the throttle body. When you spray the contact clean on an area when it drawn into the engine you may hear the rev's drop just a bit as the air leak is temporarily plugged by the liquid you are spraying. The emission at the tail pipe will smell extremely strong. You don't want to inhale a lot of that. It's bad for you....but the strong burning smell is unmistakable from the exhaust scent. You may want to have a friend post up on the rear of the car to detect the odor. When you find the spot that has the air leak you can then begin to formulate you fix, whether it's an O-ring on a fuel injector that was not put back in place or a vacuum line that needs to be reattached or plugged.
This sounds to me like a classic super lean condition that would be created by a larger vacuum leak.
Additional Possible Symptoms
Another symptom you may or may not be experiencing is this. When the engine is coming down off of it's rev's and your are not interacting with the throttle the idle may be momentarily high. This could last for a moment before the rev's drop or for a dozen or so seconds. Once the rev's drop down from a seemingly high idle speed the engine falls below that anticipated idle speed and seems to have trouble continuing to run or stalls. If you have that symptom along with the others you have described, look for air leak.