I read with interest how Fender Jaguar owners out there are pretty upset with their instrument's bridge. The common misfortune- the strings won't stay put on the saddles. On occasions, when a wicked bend or whammy adventure is done, the strings would jump off & cause severe detuning (not to mention severe embarrassment when playing live).
The simple observation here is that Jaguar saddles are the threaded version. There are no precise indentations for the strings to rest in unlike the Mustang version as indicated above.
In the 1950s - 1960s, Fender was still experimenting with bridge saddles & the threaded version did make it into some instruments like the 60s Telecaster depicted here. Unlike the Jaguar, the Telecaster observes a very acute break angle travelling to the body cavity or bridge end. The Jaguar is the clear loser here as it doesn't observe such a feature & there is simply insufficient tension to hold the strings in place if players choose lighter gauge strings for their instrument. Remember that the Jaguar & other offset models were short-lived in the Fender catalogs, no further R&D made it to the instrument prior to their passing. However, the revived Jaguar & Jazzmaster in the upcoming American Professional series (2017) will feature Mustang saddles as default 😙