My '99 VW Passat is shaking, like it's going to stall.

Best place to start is having the battery tested & replaced if needed. Then the battery cable connections cleaned & re-tightened. This is better than sprinkling with Holy water for a car.

Check motor mounts, check CV joints both of thees issues can cause the engine to stutter or shake the other possibility is a fault in the overdrive system of the transmit ion
if you have overdrive . also engin idle should be about 500 to 700 rpm normal any higher will case an abruptness .

All those codes mean a specific cylinder missfire. Start with tune up. Plugs, wires & air & fuel filters.

THAT SOUNDS LIKE EITHER A CYLINDER IS MISFIRING.HAVE YOURSPARK PLUGS CHECK, OR SENSORS

I have a 1989 5-series BMW which sometimes stalls after changing from reverse to drive. It also sometimes shakes when first driving in reverse before changing to drive.

You have a bad coil pack, they usually crack from age and heat. It's best to replace them all. Check for a VW recall on this item.

no flashing light and rough shaking will be part of spark plug but also a very bad miss fire. I am going to guess that your engine is a 1.8t if so you have 4 coils that sit on top of your spark plugs that most likely are arcing you will need to figure out which coil is failing or you can save yourself the trouble and replace all 4 and the spark plugs. before you do that though check your wireing going to your coils look for broken wires or the ground that is next to the #1 coil that is the one closest to the front of the motor and you. hope that helps. that will be the start to fixing your issue also when you pull out the spark plug look down the hole first and make sure that there is not oil in the bottom of the hole if that is the case you will need a valve cover gasket as well. good luck hope that helps

if it has a 1.8 coils are bad but check mass air meter and throttle as well

I WOULD ALMOST BET THAT THE SHAKING OF THE CAR IS DIRECTLY RELATED TO THE CHECK ENGINE LIGHT, THUS ONE PROBLEM. IT COULD BE BAD INJECTOR(S) OR JUST POOR MAINTENENCE. WITH 88K ON IT I THINK IT WOULD BE SOMETHING MINOR. HOPE THIS HELPS. LET ME KNOW. THANKS FOR USING FIX-YA. THANK YOU IN ADVANCE FOR AN HONEST RATING AS WELL.

Could be anything you need to give more info. Have the cars computer scanned for codes, It may help identify the problem or help lead you in the right direction.