I created a fresh DB and bitcoinj 0.14 (master) was seemingly able to catch all the way up. However, as soon as I stopped and restarted, I saw the following:
09:50:58.584 [main] INFO o.b.s.DatabaseFullPrunedBlockStore - com.mysql.jdbc.Driver loaded.
09:50:58.590 [main] INFO o.b.s.DatabaseFullPrunedBlockStore - Made a new connection to database jdbc:mysql://localhost/blockstore_testnet3
09:50:58.645 [main] WARN org.bitcoinj.core.Context - Implicitly creating context. This is a migration step and this message will eventually go away.
09:50:58.689 [main] INFO org.bitcoinj.core.AbstractBlockChain - chain head is at height 607429:
block:
hash: 00000000003b40109ed97aae2a6e74b2b92cf500e0b1d878e14f3dd1b06aaaf7 version: 4 (BIP34, BIP66, BIP65)
previous block: 00000000003ff55525408f562f70e5062099d9a98971c556db72c5d1b8de8a03
merkle root: 609b6cd34da964a07b007afeeb9eb07d91d291ed216fb4fbc3d7f233f0afdb52
time: [1448559924] 2015-11-26T17:45:24Z
difficulty target (nBits): 486604799
nonce: 2910893642
09:50:59.037 [main] WARN org.bitcoinj.core.AbstractBlockChain - Wallet/chain height mismatch: 607428 vs 607429
09:50:59.037 [main] WARN org.bitcoinj.core.AbstractBlockChain - Hashes: 00000000003ff55525408f562f70e5062099d9a98971c556db72c5d1b8de8a03 vs 00000000003b40109ed97aae2a6e74b2b92cf500e0b1d878e14f3dd1b06aaaf7
09:50:59.037 [main] WARN org.bitcoinj.core.AbstractBlockChain - Rollback of block store failed, continuing with mismatched heights. This can happen due to a replay.
09:51:00.665 [PeerGroup Thread] INFO org.bitcoinj.core.PeerGroup - Starting ...
09:51:00.682 [PeerGroup Thread] INFO org.bitcoinj.core.PeerGroup - Localhost peer not detected.
09:51:03.548 [PeerGroup Thread] INFO org.bitcoinj.core.PeerGroup - Peer discovery took 2866ms and returned 61 items
09:51:03.548 [PeerGroup Thread] INFO org.bitcoinj.core.PeerGroup - Waiting 2868 msec before next connect attempt to [195.154.173.26]:18333
09:51:06.421 [PeerGroup Thread] INFO org.bitcoinj.core.PeerGroup - Attempting connection to [198.11.214.146]:18333 (0 connected, 1 pending, 12 max)
...
09:57:26.690 [NioClientManager] INFO o.b.s.DatabaseFullPrunedBlockStore - Made a new connection to database jdbc:mysql://localhost/blockstore_testnet3
09:57:26.698 [NioClientManager] ERROR org.bitcoinj.core.AbstractBlockChain - Failed to verify block:
org.bitcoinj.core.VerificationException: Block larger than MAX_BLOCK_SIZE
at org.bitcoinj.core.Block.verifyTransactions(Block.java:701) ~[classes/:na]
at org.bitcoinj.core.AbstractBlockChain.add(AbstractBlockChain.java:470) [classes/:na]
at org.bitcoinj.core.AbstractBlockChain.add(AbstractBlockChain.java:354) [classes/:na]
at org.bitcoinj.core.Peer.processBlock(Peer.java:887) [classes/:na]
at org.bitcoinj.core.Peer.processMessage(Peer.java:404) [classes/:na]
at org.bitcoinj.core.PeerSocketHandler.receiveBytes(PeerSocketHandler.java:142) [classes/:na]
at org.bitcoinj.net.ConnectionHandler.handleKey(ConnectionHandler.java:223) [classes/:na]
at org.bitcoinj.net.NioClientManager.handleKey(NioClientManager.java:86) [classes/:na]
at org.bitcoinj.net.NioClientManager.run(NioClientManager.java:122) [classes/:na]
at com.google.common.util.concurrent.AbstractExecutionThreadService$1$2.run(AbstractExecutionThreadService.java:60) [guava-16.0.1.jar:na]
at com.google.common.util.concurrent.Callables$3.run(Callables.java:93) [guava-16.0.1.jar:na]
at org.bitcoinj.utils.ContextPropagatingThreadFactory$1.run(ContextPropagatingThreadFactory.java:35) [classes/:na]
at java.lang.Thread.run(Thread.java:745) [na:1.8.0_25]
09:57:26.698 [NioClientManager] ERROR org.bitcoinj.core.AbstractBlockChain - 0000000000021d8af00040ad4acec550e6299c3d78f5b730196e5088739ff807
09:57:26.698 [NioClientManager] WARN o.b.s.DatabaseFullPrunedBlockStore - Warning: Rollback attempt without transaction
09:57:27.217 [NioClientManager] WARN org.bitcoinj.core.Peer - [104.223.101.187]:18333: Block verification failed
org.bitcoinj.core.VerificationException: Could not verify block:
block:
hash: 0000000000021d8af00040ad4acec550e6299c3d78f5b730196e5088739ff807 version: 536870919 (BIP34, BIP66, BIP65, BIP101)
previous block: 00000000000003d597bcc45cac641d0e6fa02942475250307ee829726d8cf240
merkle root: 1203e8a1b12623f578cbdaba29e7946388fdb2b8099c9fb997fc2c490b5f91a4
time: [1448553454] 2015-11-26T15:57:34Z
difficulty target (nBits): 486604799
nonce: 2640845494
with 3020 transaction(s):
b1ccde412d07d5abaaed3acb807dffbf73c49cd07268a2306774269ad2d204a9: Unknown confidence level.
== COINBASE TXN (scriptSig ???) (scriptPubKey ???)
3b6c2a36577d7e050c8393f2f164baa0c3ecf7c12268e9534038f1404552d81f: Unknown confidence level.
in 0[] PUSHDATA(72)[3045022100a17555ed2639c21276a7d0e38bc384e95f7908ae82f5c91721880faef77ef9e402200ca1ebe44a601ef86573f96deac1e13344fd1725780033ba2700d78876f2f5a701] PUSHDATA(71)[304402207cdc1b545853c923a0b5a728bc6f87c847183af38ae2ac1b4c9802672b95ec41022060900711c58ae69f2f4ba9f700af82c850deb77ed93f229ca4c8fa84d273588101] PUSHDATA(71)[522102632178d046673c9729d828cfee388e121f497707f810c131e0d3fc0fe0bd66d62103a0951ec7d3a9da9de171617026442fcd30f34d66100fab539853b43f508787d452ae]
outpoint:1bba0359009c7e21051982c5dc3a737e003a682349461654a11f9d888a1c3644:1
out HASH160 PUSHDATA(20)[8931008ad3dbaf0ccc01d480efe505b5fcce76ed] EQUAL 0.01 BTC
out HASH160 PUSHDATA(20)[8ce5408cfeaddb7ccb2545ded41ef47810945484] EQUAL 40.24146 BTC
67c789c5ca43c8a088b767d54495116ebb1d78f82c940d0bf95c42cb3831c2ff: Unknown confidence level.
in 0[] PUSHDATA(71)[304402202cca8910a723e5e9ab6567e9f88b67a123acdf94f0f213f2258e0cdb8c2841ea02204b55b37727d9aee7a5bbd4059085b31051593f7bead3b040714847d8438626f001] PUSHDATA(72)[3045022100d005688d5b15ac1985ae2f127e5bc29a6dad83df4e9e0873b61c9315ffea2316022033e70ed2b1efeb3c8ec030bab7c2cb56039ce718dccc7cea39d66ad792f0289e01] PUSHDATA(71)[522102632178d046673c9729d828cfee388e121f497707f810c131e0d3fc0fe0bd66d62103a0951ec7d3a9da9de171617026442fcd30f34d66100fab539853b43f508787d452ae]
...
Seriously.