Jetta AC mixes hot and cold air

the ac core only blows cold air but You must be talking about the heater core.. In which case I would suggest that you bleed the air out of the coolant system as there is an air lock in the heater core.

Air Temperature Control Blend Door Failure No Heat or no AC (dependes on where door sticks)

In all modern cars there is a tiny DC electric motor driven gear drive that moves a plastic door that blends heated and cooled air from the AC and the heater core, this is called (interestedly enough) the air temperature control blend door actuator. The motor that moves this door fails because the door starts sticking from warping, most common complaint is no heat but it can be no AC as well. To replace these parts (blend door and blend door actuator) you must remove the entire dash from the car. Always have this problem confirmed by a dealer or qualified repair shop as it is a very expensive repair.

Other causes of no heat in the cabin are engine thermostats that are stuck open (engine runs cold) or air bubbles in the cooling system.

If you turn on your AC on one day and nothing happens, you may be dealing with a major component failure. Your vehicle's AC system consists of a compressor, condenser, evaporator, expansion valve, a series of tubes and several fans/blowers. If either one of these components fails to do their job, it may result an entire system failure. For example, if the evaporator blower motor burns out, you will get little to no airflow through the vents.
Most modern vehicles also have safety mechanisms that may prevent a component from engaging if the pressure is low in the system due to a refrigerant leak. Refrigerant can leak for many reasons, including undone welds, loose connections, corrosion, physical damage from road debris, etc. Look for oily stains underneath your car, as they may indicate a leak. If you suspect a refrigerant leak, take your car to General Automotive. We will test the pressure and use special dyes to pinpoint the leak.
Warm Air is Coming Out Instead of Cold As you get in your car and turn on your AC, you probably expect it to be blowing hot air for the first minute or two until the system cycles through enough to cool it. But what if the air never gets cold ? Or maybe it it gets cooler, but not cold enough ? No, your car didn't get confused and turned on heat by accident. There is likely a problem with your condenser.
A condenser's job in a vehicle is to cool the warm refrigerant that was used to make the air cold in the evaporator. A condenser has coils and a fan to push the air through the coils and thus cool the refrigerant. If the condenser coils get dirty or clogged, or if the fan fails, the refrigerant won't be cooled completely, so the air will come out warm. It's best to take your vehicle to an experienced AC Repair professional to troubleshoot this problem if you don't know your way around under the hood.
Cold Air Blows Intermittently So you went for a road trip or a long drive, and after 30 minutes of driving realized that your AC suddenly stopped working or switched to blowing warm air. The cold air returns shortly, and the cycle repeats itself for as long as you are driving. What's wrong with your car?
Intermittent cooling is often caused by the components of your vehicle's AC system freezing up. Typically an iced over evaporator is the culprit. An evaporator covered in ice can't cool the air, so you would have to wait until the ice melts, which is why the cold air eventually returns. There may be numerous issues causing the icing-from a dirty cabin air filter to a blocked evaporator drain or an overcharged system. Look for puddles of water under your car-this could be a sign of a freezing problem.

On the central console is the A/C module. Inside A/C module are driver's side & passenger's side air flaps for mixing hot & cold air and directed air flows towards driver's side & passenger's side according to driver commands. The passenger's side flap for mixing hot & cold air according to driver commands is bad. Flaps are actuated by electrical step by step motors. Could be damaged the flap actuator (motor), the flap mechanism (blocked in "HOT" air position), and / or electrical supply wires. You must access the passenger's side flap for mixing hot & cold air, and see what happens when you command cold air to the driver's side: flap mechanism, flap actuator, supply wires, ... Repair & replace bad pieces and test the A/C system.

Then it's not a relay you need to check but the series resistor pack inside blower housing. This controls the speed of the fan.

that is entirely possible yes, could also be a broken cable to change the temp from hot to cold, could be a problem with certain ac components under the dash

When your A/C is on the supplie of hot water to your heater core is cut off.For some reason this is not happening.It could be your heater control switch(red/blue...hot/cold)is not working,or your mixing valve that adjusts the amount of hot water that is suppied to the heater core is stuck open.

you need to have it diagnosed by a professional. These are complicated systems even to a trained tech. You may be over or under charged, have a clogged expansion valve, have a leak or many other issues. This model has a rcv refrigerant control valve inside the compressor which regulates the pressure of the compressor. If you notice the compressor never shuts off like conventional auto a/c's do the only time the clutch works is when you turn it on or off. Can be complicated.

Hi!
Looks like a classic air lock scenario! you need to perform a system bleed.
Park vehicle on level ground, when cold remove coolant filler cap. Start engine and leave to idle, turn heater to hot blower on full.
When at operating temp stand clear of coolant filler area, listen/watch hopefully gurgling and a boil over, top up when settled with very warm water/coolant, wait as it may do it a couple of times. Check for heat inside vehicle if hot and coolant settled replace cap but watch temp gauge for a while as another air lock may be in the system.
Please press the Blue button when sorted!
Paul 'W' U.K.

In addition to what emission wiz says, observe the speed of the fan when you turn on the a/c. some fans, when the are cold they run faster, then they get hot and slow down a lot. Also check that the small belt that drives the second propeller is ok. And for last, check that the front of the radiator is clear of any garbage, like a plastic bag that might have been cought in front of the condenser with the wind. If all this is working properly, there is nothing else that could be happening machanically to this a/c to stop it from cooling. look at the center of the pully of the compresor, make sure the entire thig is spining when clutch engages.