The premise of a lot of Todd's books is that there is a dragon plague in the third pass that kills a majority of the dragons. Since the dragons protect Pern from thread, the planet is screwed if all the dragons die off. In Dragonsblood, Lorana finds a cure and injects it into a Queen dragon who hasn't laid her eggs yet. The Queen goes back in time, lays her eggs which hatch and this supposedly solves the problem (I'm unsure how - it's been a couple of years since I read it and I have no desire to pick it up again)
Dragonheart takes place at the same time as Dragonsblood, but the main character is a girl named Fiona who impresses a Queen. Then she and other dragons time it back ten years so their dragons can have time to mature and heal from thread fall - which is pretty much a direct copy of Anne's Dragonflight. The only difference is that there's a plague going on in Fiona's current time, and that, rather than gloss over what happens during the time spent in the past like Anne did, Todd goes in to extreme detail about the day to day life of the people who go back to the past - and it's just not that exciting.
Other things that bugged me about the book was the fact that the main character was a 13 year old girl who spends much of the time bossing people who are her elders around. I understand she's a Queenrider/Weyrwoman, but what 30 year old man is going to listen to what a 13 year old tells him to do? Then there's the fact that she sleeps with a man who is at least 13 years her senior (she's 16 at the time that happens but still!) I understand that this is a feudal society and that young girls often end up married to men who are several years their seniors in said societies, but... ick... ick ick ick ick (Personally I do like the older guy younger girl scenario, but not when the girl is that young. If it was say a 25 year old and a 38 year old, that would be a bit different, y'know?) Plus what 16 year old is going to have the hots for a guy that much older than her? When I was 16 the only older guy I thought was hot was Angel from Buffy! I also found it silly that everyone kept saying that the dragons going back in time had to be this big secret, but what is the first thing they do when they go back in time? They tell almost everyone they encounter that they are from the future.
From the sounds of it, the rest of the trilogy doesn't get much better. I know the original series from Anne wasn't perfect and had it's issues, but Sheesh!