First, I'd like to welcome to the forum all the folks who've become active in the Choice Privileges program because they've just bought points on Daily Getaways. We've never taken a poll here, but it seems like about half the forum participants (including me) are here because of the Daily Getaways offer.
The key restriction on using Choice points is the "booking window" -- not blackout days. For domestic hotels, you're generally only allowed to book 30 days in advance. For int'l you get 60 days.
http://www.choicehotels.com/en/choic.../redeem-points
While these restrictions are usually manageable, they are a bit of a PITA because most of us make at least some of our travel plans further out in advance. One trick to get a longer booking window is to get status. With some quirks, Choice does "status match" to Platinum, which gives you a very useful 75 day booking window. I've gotten it done a few times, and it's worth the trouble to get it done. There's at least one thread in this forum which discusses the procedure.
Other than the booking window issue, Choice will generally give you "last room availability." So if you can buy the room, you can book it during your booking window. The only USA exception I've seen to this is certain premium rooms. Some Choice hotels won't let you book their fanciest rooms: hot tubs, suites, etc. Others will. Look for them when you're search a city's availability, because they represent free upgrades and the additional space can be useful if, for example, you're travelling with your family.
Overseas, there's sometimes an additional annoyance. I've seen hotels that only make their most basic room available for award redemption. Like at one Berlin hotel, it was their single-bedded room. If you wanted 2 beds, or needed room for 3, you were out of luck. Traveling in Australia, I encountered a similar problem at some of their hotels. I contacted the properties to see if I could at least pay for the "upgrade" -- the small difference between what they were selling the cheap room for and what the larger room cost. One hotel let me do this, and another said "no, you'll have to book 2 rooms." I've actually thought of complaining to Choice about this limitation on foreign award rooms, but it seems like Choice's overseas properties are managed by a different company, so "USA Choice" doesn't have much control over their allocation decisions.