First, during the miniseries,
Shortly after Baltar comes on board Galactica, Head Six reveals that a device which he had previously seen in possession of Six on Caprica has been surreptitiously installed in Galactica's Combat Information Center (CIC) (the command and control center of the battlestar). Head Six tells him it wasn't her job to put it in there. Baltar realizes there is a Cylon on board Galactica, but knows he cannot reveal that information, or indicate the device is not a part of the ship without implicating himself in the destruction of the Colonies. Baltar decides to implicate a person on board who goes by Aaron Doral because he is a civilian who has had access to the CIC during the last several weeks and, as an outsider, would be more likely to not be trusted by the Galactica crew. Having already been put in charge of testing the fleet for Cylons, Baltar informs the Executive Officer that he discreetly collected hair samples of crew members and has found Doral is a Cylon. Baltar, however, had no method at the time for testing for Cylons in the fleet. Baltar also explains he saw Doral doing something with a strange-looking device in the CIC he does not recognize.
https://en.wikipedia.org/wiki/Gaius_Baltar
Doral turns out to actually be a Cylon. It's possible that Baltar simply made a lucky guess, or subconsciously worked this out, but it does seem like Head Six gave him information he didn't have access to.
Second
In the episode "The Hand of God", Baltar successfully helps the fleet destroy a Cylon mining base on an asteroid with badly needed tylium ores for fueling the fleet. The planners of the attack ask Baltar to point out where the best target for a bomb run is on a recon photo, even though he has no idea what it looks like. In his mind, Baltar asks Head Six for help, but she tells him it is in God's hands and He will 'tell' Baltar where to point. Baltar then points to one of the buildings of the base, simply as a wild guess. Much to Baltar's surprise, his guess was correct. Baltar comes to believe the only logical explanation is that God guided his hand.
This is even less clearly Head Six giving him information; while she's the one who prompted him to guess, he's the one who made the guess. But she could have subtly guided him to the correct target.
