Let me preface this by stating that the Monster Vault style dragons are not only a huge step in the right direction, but they solve between 70 and 90% of the problem. Seriously.
Actions aren't just "how much damage can this creature do here." It's about the ability to respond to the changing circumstances of an encounter
Minor actions: The fact of the matter is that, most creatures don't get a whole lot of mileage out of their minor actions. And excluding trying to make an active perception check or insight check, there's not a whole lot of general-purpose minor actions. Thus, a solo monster only having one minor action usually isn't a problem.
Move actions: This one is surprising-in terms of real net movement, the ability of the solo isn't restricted so much in terms of not having enough move actions; after all, every move action it takes is roughly the equivalence of five move actions. The real problem is in positioning-a solo monster can only be in one place at a time.
Immediate Actions: This is where it gets tricky. Most standard monsters don't have immediate actions, but a lot of elites do. Even if you load a solo monster up with a large number of Immediate action powers, it can only use one per round. My general theory is to treat solo monsters as having two immediate actions per round-possibly taking the Demogorgon Approach (which I'll describe below).
Standard Actions: No matter how powerful a solo monster's attacks, if it only has one standard action, it can only make one standard action attack per round. If that action is somehow invalidated, you've invalidated the equivalence of five creature actions.
As I said before, the "Bonus action at Initiative Count +10" is most of what's needed to solve this problem, but it has to be for all solo monsters. It cannot be seen as "a feature unique to dragons" because this is fundamentally an issue not of just some solo creatures, but of the basic concept of solo monsters in general. In addition, it pays to look into what that bonus action is.
Unless you're using the Demogorgon Approach (again-see below), a solo monster's bonus action doesn't usually come with a move action or a minor action. This means that the creature is, for all intents and purposes, getting a bonus turn each round where it's dazed, and the same dynamic applies. If the creature is melee-only and you can prevent charging (Slow, Immobilization, or simply being exactly one square out of reach), the creature has no means for attacking. This is the crux of the advantage in designing a solo monster that you really don't have in designing a regular monster: you can make a solo monster's bonus attack wildly more powerful than the numbers themselves would recommend, just so long as the party is given some means of counter-acting this ability.
Take the Catastrophic Dragons, for example. Their auras are nasty, certainly, but the real heavy hitting powers are when the auras explode. If you have a solo monster that, on its bonus initiative count, always makes a Close Burst X attack, or makes a melee attack, then the party can plan around this-withdrawing as needed. Note that this is much easier said than done. Most characters don't have a spring attack mechanism, and excluding Master's Wand of Magic Missile, there aren't a lot of at-will forced movement effects. Thus, a party has to come to terms with whether or not it wants to eat that bonus attack, or take the methods needed in order to negate it. If the attack is arbitrarily powerful, then you can bet the party will take the steps needed to negate it. On the other hand, the steps needed to negate the attack may itself be game breaking-most players can't easily withdraw from melee without at least provoking an opportunity attack, so make sure not to be too unreasonable.
Again, it's been my experience that the best solution is to use close burst or "attack all adjacent" type attacks, but rather than balancing the damage output for multi-target, balance the damage output for one target. This way, the party will space itself out in such a way that only one melee unit needs to actually be able to be hit at a time, but they can alternate-move hit, ally hits, then moves, so on and so forth. Again, you can potentially trigger a lot of opportunity attacks using this method, so don't go too overboard.
Of course, the alternative is the Demogorgon approach. In short: Build a creature like an elite, but give it two full sets of actions. The result will be a creature that is MUCH faster than usual (effectively having 10 move actions per round!) but otherwise is similar in function and ability to respond to changes in an encounter to a pair of elites. I recommend this approach when designing monsters intended to have extremely high levels of agility, or-of course-dual minded thinking.