The following are initial findings, but it's a good place to start:

Members which need a mutex protecting them:

• conversations
• timeout_jobs

Members which should be removed. Instead check_update() should probably return a context to be passed to handle_updates():

• current_conversation

• current_handler

• All other members must be set internal (i.e. renamed to be prefixed with __) so they won't be modified after __init__().