From my perspective, any of the problems that people had with M&M1e were addressed and corrected in 2e.
I believe there's a review by one of the ENWorld (ir)regulars that goes into a lot more detail, so I'll just hit the highlights.
Powers-as-extras are gone, helping to reign in some of the more over-the-top character builds. Instead, you pay for "extra" powers tacked onto the main power (such as variations of a Blast power) by paying 1pp for the Alternate Power feat, but the trade off is you can't use both powers at the same time, only one or the other.
Strength and Dexterity no longer provide a bonus to attack or defense rolls.
Feats are reduced to 1pp each, and several of them have multiple levels.
Skills are now bought at a rate of 4 skill ranks per 1pp, making Batman-type/skill-heavy heroes much more feasible.
Super-Attributes are removed entirely, using the regular d20 Attribute scale. Super-Strength is still around as a power, but the function is entirely reworked (gives a bonus to Strength for lifting and to grapple checks).
Powers are no longer strictly limited to your hero's PL (some can wildly exceed your PL. For offensive and defensive powers, you can choose to trade-off in favor of either attack bonus vs. damage bonus (for offense) or Defense bonus vs. Toughness save (for defense).
The powers in and of themselves are a lot more versatile, and the rules for Devices and Equipment have been greatly improved upon.
Also, characters are no longer strait-jacketed to 15pp per PL, making it possible to build an effective Superman that's not over PL20 (I've seen Supes builds w/ PL as low as 14 on the Atomic Think Tank).
I started w/ 1e M&M, and I can't recommend switching over to 2e enough.