You're right that it is generally a good thing. If you can move into the next area with a free technology (from a social policy or wonder), that's definitely a good thing.
The only downside in general is that technologies in the next era will be more expensive than ones in your current era. So if you push too hard to move into the next era, you may end up having to wait 40+ turns without any technology advancements. This can leave you at a significant disadvantage against opponents that may now be an era behind, but who have been enjoying the benefits of all the technologies from the current era for quite some time.
Also, rushing an era can sometimes affect tourism output. Some theming bonuses require 2-3 great works created in the same era. You may want to delay an era for a few turns to time your next great writer / artist / musician to achieve these bonuses.