I have used Asana for years always wanting to like it. It's almost what I want and it's nearly done right. I think this is it for me though. Don't think I can look at those serifs for very long. Overall the design just feels way overwrought and without any clear organizing idea. The margins are all over the place, there are lots of controls that are way too small. The page looks messy and difficult to focus on. To wh…
Typographically speaking, Amasis (the serif type now being used for headlines) is an odd choice for a pairing with Proxima Nova (what they are continuing to use for everything else). It looks a bit awkward at the size and weight they have it because it's actually a slab serif (check out https://www.myfonts.com/fonts/mti/amasis/) and the slabs turn into slightly chunky serifs on standard-DPI screens (though it does look a bit better on Retina). This, combined with a similar visual weight to the other text, contributes to the lack of contrast you describe.
What I'd advise is either bumping up the weight on Amasis to increase the contrast and disambiguate the slab serifs, or better yet, switching to a nicer overall serif type such as Hoefler & Co's Mercury Display (http://www.typography.com/fonts/mercury-display/overview/).