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Several conversations that take place in The Ragged Flagon state that he is in a relationship with the RedguardThief, Tonilia, though both seem to have different views as to where they want the relationship to go. In a conversation between the two, Vekel states that he wishes she would slow down and live with him. Tonilia's answer is that she is just fine with the way things are. In another conversation between Tonilia and Dirge, it is stated that he believes Tonilia is cheating on Vekel with Brynjolf, though she quickly denies this, telling Dirge to mind his own business.
Even if the Dragonborn gains the rank of Guildmaster, he will still refer to you as Brynjolf's protege. After becoming the Guildmaster and asking him about what's the word around the Guild, he will say that they have a new Guildmaster but doesn't seem to acknowledge it being the Dragonborn. The same also goes for others in the Flaggon except for Delvin Mallory.
PC 360 PS3 There is currently a glitch with his quest in which after collecting the four journals they will stay in the Dragonborn's inventory and 4 units of weight will be added, but no reward or other items. The weight is as a result of the journals becoming no longer quest items and thus contributing to the total weight now that they are sellable/disposable.
It is also possible to start the quest without even being a member of the Thieves' Guild at all. By entering Yngvild and acquiring all four books, the Dragonborn will be given the miscellaneous objective "Return to Vekel". Upon returning talk to him and he will have all the same dialogue options as if he originally asked to retrieve the books.