MD-82
Aircraft Equipment Problem Less Severe
General None Reported / Taken
Aircraft; Airport
I was [advised by management] to give my account of a recent flight and approach into MEX. We started  a little over two hours late due to a battery charger problem maintenance delay. I was flying with [a first officer] who had not been to MEX airport in a long time. She said she watched the [special airports] video and reviewed the NOTAMS so she was aware of the FMS dead reckoning problem and that SMO VOR was out. I told her that I had been in there several times lately and once en route we talked about the arrival into there and she asked great questions. I told her how they have a tendency to keep you high on descent and that it's important to be at 160 kts inside SMO and that we would need a vector to intercept 5R LOC since the FMS goes to dead reckoning inside SMO. Since we were so late; 5R was closed and we were given the VOR/DME 5L approach. We were asked by approach if we could do the approach on our own and we told them we would need a vector to intercept. On intercept heading the FMS went to dead reckoning followed shortly by a NAV fail warning. We continued and intercepted the MEX VOR 053 course inbound in raw data. Shortly after starting down from PLAZA FAF we picked up the runway and landed. If I could give any advice to crews flying into MEX; especially someone who has not been there before or not in a long time [it would be] to talk about the arrival en route and be prepared for almost anything. Visibility on even good days is usually marginal and language can be an issue. Whenever possible it would be good to have FMS planes that don't have the dead reckoning problem. Hope this was of some help.
On final about 400-500' [AGL] we got the LOUD 'pull up terrain' warnings. The runway had been in sight for some time. We continued VFR to land 5R for a normal landing. The #1 flight attendant said she heard the warnings as did some or the forward first class pax.
An MD-82 flight crew operating into MEX received DR (Dead Reckoning) and NAV fail warnings while on a visual approach.  Because they had briefed the possibility of these issues they were on raw data VOR navigation.  The First Officer advised that inappropriate EGPWS warnings generated due to the loss of positional information were heard by the passengers and a flight attendant.