How accurately is engine thrust known? It could all boil down to something as simple as F=MA - if you know any two of those, you can instantly derive the third. If the aircraft knows that it's putting out so many kilograms of thrust and it's accelerating at so many metres per second squared, then it's effectively weighed itself - and will be able to spot that it's operating outside the safe envelope, or if the input weight to the FMC is at gross variance with the empirically derived figure. Much simpler than arcniz' proposal of monitoring multiple factors during take-off, but perhaps useful nonetheless - and automatic, which may be a bonus if you drop the stopwatch.
Couldn't such a system be achievable with some extra software in the existing FMCs and no hardware changes at all? Not being anything other than an armchair consumer of avionic information, I don't know how the calibration would work or whether there'd be any point in trying to derive the normal operating parameters of the aircraft by routinely monitoring performance and building up a database of observed readings, but the physics is at heart as simple as it gets.
Perhaps this might be a quick yet effective first step in catching this class of accident. I could even see it being a task that something as simple as a PDA with GPS could cope with (but that's not to understate the problem of false positive alarms). A full TOPMS system has to be a good idea, but sometimes you get a lot of the benefits of a complex idea with a relatively small core feature set.
R