I've been cherry picking my way through the modern Doctor Who episodes after getting burned my some of the early Eccleston ones- which in practice means that I've been watching the ones written by Steven Moffat.
I have now watched up through Blink and I have loved all of them. Aside from a few early Eccleston ones, I have now gotten this far only watching only the Moffat ones and I fear that I'm selling the rest of the episodes short. Are there any other great standalone episodes that I should check out or should I indeed just move on to "Silence in the Library"?
If you're talking the first three seasons, then there's quite a few. Father's Day is a gut punch, the Bad Wolf two-parter has a killer back half, School Reunion is an excellent episode that sets up a lot of the themes that New Who often comes back to, The Impossible Planet has an awesome, bleak atmosphere to it, Gridlock is one of my favourite, richest episodes ever, and the Human Nature two-parter is a stone cold classic. These often do have strands connecting them to other episodes, but they can easily be enjoyed on their own merits.
Silence in the Library, good as it is, isn't the best of series 4. That honour goes squarely to Midnight, and I highly recommend you track it down. Turn Left is superb, but sort of needs some knowledge of other episodes. The Unicorn and the Wasp is, IMO, a superb comedy episode, but opinions vary on it. The Fire of Pompeii is a bit of an epic, too. Out of the specials, watch The Waters of Mars.
If you plan on watching Moffat's series, definitely watch Silence in the Library.