There's over 30 years of papers and academic research on anonymous mailing systems and Bitmessage incorporates not one of those concepts
Regardless of implementation details, the purpose of bitmessage is interesting and any secure alternative would make a great communication software.
So no, you are not necessarily fine.
Anonymity protocols are mostly divided into 3 classes: broadcast (dining cryptographers, buses, bitmessage), mixes/rerouting (mixmaster, mixminion, tor) and private information retrieval (dissent and followups).
After decades of work in the field , bitmessage implements broadcast in the most naive way: floodfill. Global passive adversary can simply find out where the message appeared first. If the message is encrypted with a key which is only known to the receiver (i.e., message is not for chan), everything is ok. But in this case bitmessage is not better than alt.anonymous.messages.
If messages can be linked together, active non-global adversary can measure time and exploit dynamic topology of the network to reconnect closer to the sender. Bitmessage offers no protection against it. With alt.anonymous.messages the solution is remailers, and bitmessage offers no alternative.
Streams are not implemented, so bitmessage does no scale.
As you can request a list of neighbors from anyone you can easily attack network by constantly reconnecting closer to the message sources. For example, you can track down all active users of some particular chan.
Freenet project did a lot of work to protect against opennet attacks, and bitmessage completely ignores it.
But, given the possibility of something like this happening either way, this is why clean open protocols are more important for decentralized software, than reference clients.
at the cost of getting scorned, but dead serious: a controlled backdoor, with an automatic audit trail, to be used by lawful agencies for keeping us safe. Bitcoin by design supports criminal activities, which undermine the community. A community messaging system should have a way of cleaning itself.
Probably not the example mentioned by Parent, though.
No one has ever asked if I would backdoor it. I certainly wouldn't; that would defeat the purpose. Someone below linked to a random user requesting this feature:
Perhaps that is what you remember reading.
What is questionable is the security of the sender.
I doubt proof-of-work can really help against determined attacker. Spammers will happily calculate proof-of-work to send spam. Spamming chans is really easy and all chans will be flooded with spam once it is worth the effort.