First of all, I can totally understand your frustration. Losing the integration between the map view and the tile animation and tile collision editors is probably the biggest downside of Tiled 1.0, and it doesn't sit well with me either. The reason it was released like this anyway is because I couldn't come up with a nice alternative yet and in the long time that this change was available in the development snapshots nobody had complained.
But, we need to find another way way. The change was made, because tilesets now have their own undo stack, which was necessary to enable editing of external tilesets. This becomes problematic, when both the map and the tilesets can be edited in the same view, because it was no longer clear what action "Undo" should apply to. Hence operations affecting the tileset were taken to the separate Tileset Editor.
I think there could be some solutions while keeping the current workflow:
Add a quick way to go from Map Editor to editing a certain tile in the tileset editor, for example by putting actions in the context menu of a tile "Edit Tile Animation", "Edit Tile Collision". These actions could in addition be included in a "Tile" menu when right-clicking a tile object on the map. They would switch to the tileset editor, select the tile and open the respective editing mode.
Tile animation preview could be added to the tileset editor. You would only see each animation once, but that would already help when multiple animated tiles need to animate together.
When the tile animation editor is really brought back to its previous place, it would also prevent better integration with the tileset editor (as done with terrain and collision editing). This was something I still planned on doing.
In any case, please let me know what you think of these ideas and maybe you have some ideas as well.