Its often the harmonics that cause the problems from phone masts, but biggest culprits are two way PMR radios, used by Taxis, and emergency services.
Transmitters are generally pretty clean - a 200W mobile phone BTS will not have a spurious that's anywhere near to drowning a 10mW car remote, and they're up at 900 / 1800 MHZ anyway, with tuned antennae that further attenuate spurious emissions.
Whether the receiver is desensitised in the presence of a strong signal-even this far out of its' passband is another matter.
I suspect the main cuplrit is PMR and particularly Tetra systems that are starting to creep up to that part of the spectrum, especially as RF remotes are generally basic AM transmitters that are badly affected by the bursty TDMA structure of a Tetra transmission.
Even then- as in 99% of interference, IME, it's the receiver or its' installation to blame, despite the perception that it's the transmitter that's doing the interfering. Ask any frustrated radio amateur! receivers are designed to work acceptably in typical conditions so if you happen to be next to a base station, a police station, a radio amateur, CB'er, etc. All bets are off. They won't have spent the money to guarantee that your receiver is good enough.
They have got better because that goal has moved. There are more wireless devices around than there used to be so the performance required has increased. There still are, and always will be, scenarios in life that will challenge them.
Thank goodness the Omega has a cylinder lock too.

Kevin