What's with the long series of regular, ~5000 BTC transfers?
A very expensive attack on the network.
I very much doubt that, even with that many transactions all they are doing is giving the miners money in the form of transaction fees, all of those transactions combined add maybe 100kb to the block chain.
Whats even more the current Bitcoin client has multiple anti-spam measures in place. The more often you transfer the same coins the lower priority they become for inclusion into a block and transfers take longer. So if you transferred the same coins between two addresses you would quickly get to the point where it took days to transfer those coins, if you waited a while they would return to normal. To actually attack the network you must offset this priority lowering you get when you transfer the same coins, to do that you need ever larger transaction fees that will whiddle away whatever coins you are using to attack the network and give them to miners. Very small transactions require transaction fees to prevent spamming of tiny 1 santioshi transactions. Overall the anti-transaction spam measures are very through and more than sufficient.
how do such bogus transactions vanish? is there some kind of TTL?
Invalid transactions are not rebroadcast by peers, if you are running the client on your machine you probably never saw this transaction and the monitor only saw it because of how well connected it was, this transaction will not be included in a block and has probably already faded from the network, having only been broadcast to very very few people and stored by none.