For a long time the only block explorer for testnet has been the original
blockexplorer.com, which is unfortunately often broken / behind / slow and
not really maintained any more.

There is now a new one, here:

https://www.biteasy.com/testnet/blocks

There's also a REST/JSON API for it.

Please note one curiosity of this block explorer is that the coinbase tx
doesn't necessarily come first in the listing (it's sorted by "time
received", see).

Other interesting thing to note: this site is built using bitcoinj. The
author can be contacted on IRC sometimes using the nick damethos.