Location Library: just XM0110, or any SiRFstarIV?

Yes, the GPS claimed that the fix was valid.

There was no way of detecting this problem from the data itself (other than comparing against previous known good data).
DOP values and everything else indicated everything OK and good.
Plotting the data on a map shows that it even stays in the area of the incorrect position for a while before jumping back or jumping to a new incorrect position.

In our case the sequence was always like this:

Unit was going from area with good signal to area with bad signal
Fix was lost temporarily
Fix was restored
Fix was randomly after that way off
Proper position restored when signal was good again.

We have a temporary solution in place:
As soon as fix is lost, power off the GPS module and turn it on again.
Doing this clears any data that is used for fix in bad signal conditions and good signal conditions are necessary to restore fix again.
The downside of this is of course that it takes longer time to get a new fix if it is lost temporarily.

Using same antenna but SiRF III based GPS instead under the same conditions, fix was only lost and didn’t come back until signal was good again.

We had to convince the manufacturer to actually test and reproduce on their own before they escalated it further to SiRF/CSR.