My car senses that the door is open when it is not

There is a sensor attached to the door latch that senses the door opening, it may be defective.

The door ajar switch is likely defective, it senses the door is open ad turns on the coutesy lights as well as alerts you to the fact the door is open and the key is on (door "ajar").

Door ajar switch problem more then likely or wiring issue . The BCM - body control module won't turn off interior light , let door lock because it think's the door is open . The door ajar switch is a input to the BCM .

The first thing would be to have it checked for DTC'S - diagnostic trouble codes . Also check with an enhanced scan tool to see if the BCM shows ajar switch data (open or closed ? Do you know about body electronics ?
Body Control Module
The various BCM input and output circuits are described in the corresponding functional areas indicated on the BCM electrical schematics. The Body Control Module functions include the following:
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A/C compressor request. Refer to Air Temperature Description and Operation

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Remote Function Control. Refer to Keyless Entry System Description and Operation

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A/C cooling Fan. Refer to Air Delivery Description and Operation

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Audio Delay Power. Refer to Radio/Audio System Description and Operation

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Exterior and interior lighting control. Refer to Exterior Lighting Systems Description and Operation

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Daytime running lights (DRL)

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Automatic lighting control

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Fog lamps

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Interior lighting. Refer to Interior Lighting Systems Description and Operation

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Battery rundown protection (Inadvertent Power). Refer to Interior Lighting Systems Description and Operation

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Chimes. Refer to Audible Warnings Description and Operation

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Key-In-Ignition

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Head Lamps On

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Seat Belt Not Fastened

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Turn Signal On

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Park Brake Warning

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Door Ajar Warning

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Check gages

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Gage control. Refer to Instrument Cluster Description and Operation in Instrument Panel, Gages, and Console.

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Instrument cluster indicator control. Refer to Instrument Cluster Description and Operation in Instrument Panel, Gages, and Console.

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Theft deterrent. Refer to Theft Systems Description and Operation .

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Engine coolant level sensing. Refer to Cooling System Description and Operation .

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Washer solvent level sensing. Refer to Wiper/Washer System Description and Operation in Wipers/Washer Systems.

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Key-in-ignition sensing. Refer to Audible Warnings Description and Operation in Instrument Panel, Gages, and Console.

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Seat belt use sensing. Refer to Seat Belt System Description and Operation .

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Brake fluid level sensing.

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Parking brake state sensing.

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Rear compartment interface. Refer to Power Door Locks Description and Operation

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Horn interface.

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Door lock interface. Refer to Power Door Locks Description and Operation

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Bulb Check. Refer to Instrument Cluster Description and Operation in Instrument Panel, Gages, and Console.

Its sensing that there is a key in the ignition. You have to replace the switch in the ignition cylinder that senses a key is inserted. Or alternatively access a wiring diagram and cut the wire from the key sensor to eliminate it.

Something wrong with the rubber covered pin on the door or the plunger/switch on the door frame that senses whether the door is open or closed.

More than likely one of the doors door jam switch is at fault.It is more than likely the drivers door sense it is used the most.

This Van has a system in it called delayed exit, this means the radio and other accessories stay on for a time as long as none of the doors are opened, when the door is opened the module senses that switch in the door is activated and shuts everything off. The easy way to test this is open the passenger door, if all shuts off you found the problem, the driver door switch is defective. the switch is attached to the door lock inside the door.

U have a defective door ajar switch most likely, if this switch remains closed then the delayed exit feature stays on, this means the radio will stay on because the delayed exit module didn't sense the door was opened, try opening the passenger door to confirm this problem, any door should turn off the radio

Check the operation of the door sense switches, they may be sticking.
Check domelight switch is in correct position to enable auto door activation (if applicable).

The door catch/lock mechanism on the MX5 is liable to do this occasionally - if you keep trying to unlock it, it will open eventually (I manually pop the internal lock whilst opening the outer handle if that makes sense).

Once it's open though, you pretty much need to open up that door and replace the lock mechanism.

Hope this helps,
Sherwin