My e46 bmw has some warning transmission light switched on the car judders when it changes gear im badly worried what it could be it was fine when i drove early was parked up for 15mins car switched off when i started it this bloody warning light had switched on

THE SOLENOID PACK IN THE TRANS IS BAD

try filling up your overflow jug just a little more but as long as temps are ok, no worried. I had a vehicle do the same thing...

Sounds like your transmission is bad. You'll need to take it to a shop to have it checked out.

Don't worry I'm sure you will get the solution of your problem, just check the link I attached
Bmw e46

You say that you plugged the battery back in. Did you replace the battery or did you have it disconnected while working on the car? What repair were you doing?
These transmission computers are extremely sensitive to the condition of the battery. If the voltage dips at all, they start acting up. If this is the original battery on an 8 year old car, I would replace it as preventative maintenance before investing any money in having someone look at it. They would want to replace a battery that old before doing anything else, and it will cost you a lot more if they do it. If that is the problem, the light should clear itself after a few start cycles.

this is the check engine light does it come on then off? did it stay on? if this light is comming on any one of a hundred or more thing can cause it. from a loose gas cap to a sticking sensor. you might want to have it hooked to a computer to see what is causing it might be a minor problem like low washer fluid and it could be the start of a serious one. these lights remind you of scheduled maintinance,low fluids,oil changes ect depending on the manufacturer standards.i would check all of the fluids and if they are ok then get it checked better to be safe than sorry

The vehicle owner's manual will contain that information.

if the transmission was low on fluid you may have worn some parts,take this to a shop that specializes in BMW transmissions,this is not for the local transmission guy,special tools needed to test the transmission,may have to be re-programed

sensor needs replacement or ABS module

bad throw out bearing,  You clutch is on the way out.