Edited for Syndication: Specifics for the Bergeron era: Because many episodes each season offer special prizes and sweepstakes (usually for chances to win vacations around the world, sponsored by Disney), many reruns are edited in one of two ways - earlier episodes simply fade to commercials before information for such prizes and offers can be seen; more recent episodes simply plaster a disclaimer at the bottom of the screen stating the offer is no longer available.
For the Bob Saget episodes, Saget speaking with the winners are usually cut out. So, nowadays we see Bob Saget announce the winner, and then it abruptly cuts to Bob Saget doing his sign-off gag.
Old Shame: It's possible the Fuentes/Fugelsang era is this, as those episodes aren't shown on television anymore. Also, during the 20th-Anniversary special (where Bob Saget returned), neither Fuentes nor Fugelsang were invited to intend, and neither were acknowledged at any point during the special. Bergeron did briefly mention them during the "300th Show" special, and some clips of their host segments were shown, but that was it.
Episodes from this era are sometimes shown on WGN, but very rarely and usually only before baseball games.
Reality Subtext: Saget's last two episodes did not have him do the "And honey..." closer. By that point, his marriage was crumbling and eventually resulted in a divorce.
Recycled Script: Recycled clips, to be specific. As early as the Fuentes/Fugelsang era, old clips were being shown alongside fresh ones, albeit with new commentary. Most of the music montage segments were built on editing old clips together since the show's earliest days. Slightly justified in that the show is not as popular as it once was, and combined with the rise of online video (it doesn't just cause Network Decay!), it's reasonable to assume that the supply of fresh material has dwindled. Only fresh clips are eligible for the weekly prize.
Technology Marches On: Yes, you can still send a tape or DVD to the famous "Box 4333, Hollywood, California, 9-double0-78" address, but now you can also submit a clip via the show's website, which undoubtedly helps the archivists and producers considerably.