IMO the best mechanic from 4th ed. Healing surges have returned. Unlike 4th ed healing surges, you roll to regain the HP rather than just get back a set number. Of course, any DM could easily say "you take the average of the roll rather then roll" and now we've got 4th ed healing surges.
Another difference is that instead of getting a fixed number of healing surges across the entire span of your career, it scales as you go up in level, granting you more and more healing surges the higher level you get.
No Stat Penalties for Races
Every single edition of D&D has had ability score modifiers that included negative values depending on your race. That is not the case in 4th ed where you ONLY get positive modifiers. This has continued to D&D Next.
Trained or Not Trained in Skills
3.5e had a highly detailed method of determining how much training you had in a particular skill. 4th ed simplified this dramatically by treating it as a binary value. Either you are trained in a skill or you aren't trained in a skill. D&D Next has continued this method of determining your bonus to skills.
Reduced bonuses to attacks
3.5e had a highly detailed number of variables you could add to your attack modifiers. 4th ed consolidated a lot of these benefits by introducing the concept of combat advantage. 4th ed still kept some different types of bonuses. But a lot of them were reduced by simply granting combat advantage.
D&D Next has continued this methodology by simplifying bonuses even further by simply granting advantage or disadvantage.
Basic NPC Creation
4th ed treated NPCs and monsters as the exact same thing. They were created in the exact same manner. One look at the bestiary tells you that D&D Next is continuing with this methodology. While we do know there will be optional rules for using a 3.5e style of creating NPCs, that isn't going to be the only way, or even the default way.
Martial Characters with Unique Powers
Fighters in 3.5e got extra feats. That's it. 4th ed gave them unique powers that only they had access to. D&D Next has continued this by giving fighters unique maneuvers that only they can use.
The idea of giving casters spells they could use all day long was a development pioneered in 4th ed. It was so good that Paizo stole the idea and used it in Pathfinder. For me the idea of 0th level spells not being at-will is mind-boggling.
D&D Next has continued this idea by granting all casters at-will spells.
Because of the massive change in spell structure from Vancian to AEDU, 4th ed captured a lot of the utility spells that come up a handful of times in a campaign by making them rituals. These are spells that do not take up your in combat resources for out of combat benefits. Rituals removed the need to decide between an alarm for the day or an extra fireball.
D&D Next has continued this by allowing spells to be cast as rituals.
Healing as well as fighting
Many people consider clerics healbots pre-4th ed. It doesn't gel with my Pathfinder experience, but it's a commonly held belief. 4th ed changed that by allowing healing powers to be cast as a minor action allowing you to still use a damaging power.
D&D Next has continued this through the use of the "word of power" condition on spells. Essentially a spell that has "word of power" is a minor action allowing the cleric to do something else on their turn.
Are all developments from 4th ed in D&D Next? No. Martial abilities are on a different resource management system to spells. But many of the 4th ed developments are part of D&D Next. So I disagree with the notion that 4th ed has been thrown under the bus. While D&D Next isn't simple a 4th ed clone, it does contain many of its innovations.