The cities being laid out in a grid looks nice but is ultimately far more difficult to understand then just looking at an alphabetical list in a dropdown. Auto-picking your departure city based on your current location is admittedly a nice detail, but it wasn't immediately obvious how I change where I'm starting as the "link" was different than anything else on the page.
The "Who's Flying" section is massive for having so little real information. And why are that the font is 120px (or 12rem) but the "+/-" controls are faded out and tiny by comparison?
The calendar is again completely oversized, low contrast, and difficult to understand. My laptop has a 1440x900 resolution screen and I can barely fit a single full month in the window. If I happen to want to buy a ticket more than a month or so in advance, I need to repeatedly click "More Dates" which then appends another two months to the already crazy long page? Also, the low contrast purple highlight for all the dates inbetween departure/return isn't immediately noticeable.
When I click on a ticket price another window slides up over it - took a few moments to figure out what actually happened there. Overall the "ticket selection" again looks pretty, but when I can only see a few in the window at any given time it's far less usable than a standard clean list. Also, the "Continue" button looks identical to the other addon options, and it isn't immediately obvious how to progress if you don't want to upgrade your ticket.
The seat selection admittedly is admittedly fun looking though why are half the faces looking upset? Also, versions of the seat selection where they actually place the seat INSIDE the plane in it's real physical location are more readable than this abstracted version, though I do like how they clearly broke it up into sections that show the different cabin/seat types. Again though, I can only fit about half the plane on my screen at any given time.
Having the form adjacent to the seat selection is a nice touch as you can then easily track who's sitting where as you enter their information (especially if you're a family with kids), but for some reason they neglected to highlight the seat on the visual map. Also, the form is again overly tall and I can only fit about 2/3 of it at any time.
Overall I think it's a good start but hardly production ready. My gut instinct is that most people will be impressed by how "pretty" it is, but that the overall conversion rates will decrease significantly. The one really well done idea is the fixed header, though realistically it should progressively fill out with information and not show/hide ticket info at different stages in the process (for instance, it did show my takeoff/landing times and price which was extremely useful, but now hiding that to ask me who's sitting in seat 4B, which is already emphasized at the top of the form).