When I unlock the 02 Mondeo with the key, it disarms the alarm. I can't do this on the 06 Mondeo without the alarm going off. I have to use the remote to open, not something I want to rely on.

Is this standard for the later MK3's?

here is are two quotes from another forum.

"I was told that the Mondeo has a thing where, if you unlock it using the
key manually in the door handle you get a certain time to start the
engine, else the alarm goes off. Its designed to stop theiving chav
ripping the handle off the door and gaining entry. Hence if another door
is opened whilst you're between door lock and ignition it sets the
alarm off straight away."

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"Mine is a 2003 model, and if I open the door with the non-remote key it
starts bleeping then the alarm sounds. The handbook says you have to
move the key to position II but mine only stops the alarm if I start the
engine. Same applies to a friend's 2004 model.

The handbook is not very clear which model that particular instruction refers to."

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Have a go and see if that works.