One of the things missing at LinkedIn messaging itsel (and thus could be a game changer in here), is the ability to "reply" to a message.
I imagine like you could click on a message and "quote" it before adding your own response, so like this you can respond to individual messages. Especially if you're in a lively conversation it could be difficult to send a proper reply and make it easy to see to what it relates.
Would love to see this implemented in here.