Despite all the discussion of the difference between tiers of play, it has been noted that 11th level PCs won't be radically more powerful than 10th all of a sudden. As we've seen glimpses of, it appears the primary difference is that 11th characters will be able to choose from Paragon choices (maneuvers, spells, racial traits and such). They're not getting all the choices at one single level, though. The 11th level PC will have perhaps one or two Paragon traits to choose from, most likely.
The scope of adventures described as different between Heroic, Paragon and Epic is intended to be a generalization. There's no need for any drastic changes in play the minute any PC gets to the next tier. However, the encounter and campaign design notes in the DMG will likely note how to introduce new styles of challenges to the PCs. The choices available from the Paragon lists will likely include various "game challenging" abilities, like flight, long term invisibility or planar travel. Thus, a DM should be aware that these will begin to appear in a campaign in the PCs hands as they do achieve a new tier. I assume that a number of the abilities in a tier will be well suited for the kinds of adventures described as appropriate for that tier. Thus, since Epic is described as when planar free wheeling takes hold, Epic might be when plane jumping traits allowing long duration travel start appearing the hands of PCs. Before that, the DM would have control over planar travel through portals, rituals and NPCs. In Epic, it would expected that PCs could slide between planes in an adventure and hopefully writers and DMs will be prepared for that.