This post will be focused on UI elements and design, as well as user experience as a whole. It goes without saying that significant portions of this will be personal preference and opinion, although I will try to remain as objective as possible.
Based on what I've read from other user comments, there may be a bug regarding toolbars not showing up at all upon loading C3. I have experienced one time myself where after switching back to the C3 tab, my properties bar was empty. Going back to the layout view fixed it, but it was odd. I was unable to reproduce the issue.
While accidentally closing a toolbar is really relatively easy to do, bringing them back seems be more difficult/hidden than it needs to be. I don't think there needs to be so many submenus to get to them (Menu -> View -> Bars). I'm also not sure what the Addon manager is doing in "View", it could probably go straight under Menu. Then "View" would just be Start Screen and Bars, which probably no longer need their own sublist. It would also be nice to make it a little harder to close a bar on accident - traditionally one way around this is to have a confirmation dialogue when clicking the x ("Are you sure you want to close?"), but I detest those. A better solution might be to have a little temporary "Undo" button show up after closing one, that fades away shortly. Personally I think the "X" to close should be simply be removed, and leave right clicking (long press?) the only way to close or undock the bars.
On a positive note, the design for bar placement and docking is absolutely fantastic!
I like how the free edition limitations are communicated, and it is intuitive to get to them. What isn't clearly communicated is that you can get more maximum events for logging in or verifying your e-mail. It is also unclear that the email can be or needs to be verified at all.
Worse, even though I know this, I was unable to actually figure out how to verify my email. Going to my profile shows that it is unverified, but offers no method to remedy the situation. Edit: A reverify link has appeared! But FYI the email got sent to spam for gmail, with the reason that construct.net is known for sending spam. Perhaps you may want to contact the gmail team regarding your acquisition of the domain.
The save button only shows options for cloud saving. I imagine a new user might find it difficult to realize local saving is an option at all, as it is once again buried under submenus. It would be great if the interface for cloud/localstorage/download save were unified.
I have a lot of complaints about the event sheet/layouts tab system (also an issue in C2), but I will leave that for a followup post.
Visual comparison between C2 and C3
I'm glad the Microsoft Office style toolbars at the top are gone, I wont miss them at all! I also really like the change to the bottom status bar - the information provided is more immediately noticeable/accessible. It is only really relevant on the layout view anyway, so it doesn't always need to be on the bottom as it was before.
I hope a dark theme will be available in C3, it is much easier on the eyes for people who spend significant time in front of the monitor.
I have mixed feelings regarding the spacing/size of the text in the properties bar. While white space looks very nice, in this case I think I prefer the utility of having a more compact spacing. The bigger complaint I have is the behavior of line breaking. In C2, if the width of the property bar shrunk and there wasn't enough space for the text, the text would get truncated with ellipsis. In C3, they wrap to the next line, which leaves some properties with one line spacing and some with two, which looks really bad in my opinion. This was actually one of the first things I did, as the property bar in C3 is significantly wider than in C2, I sized it down a bit.
The next one was an issue I had with C2 as well. It is a small thing, but I found it strange that when nothing is selected the layout properties are shown by default. I always felt it would make more sense to show the project properties by default, especially as you can have multiple layouts and they can be selected in the project bar.
Sorry for the long post about first impressions! I have additional feedback for the image editor interface as well as the tab system I mentioned earlier, to be provided in the near future.
Edit: Followup on the toolbars - I found the reset layout in settings, but it asks you to restart C3 for changes to take effect. Is that really necessary? And I'm assuming by restarting C3 it means refresh the page, and when refreshing the page there is a dialogue warning that things might not be saved, but no direct way to save from there. This could probably use some work to make it friendlier.