Is there a way to group Channel fields when displaying it in the Content section in EE's CP? A way to visually group related fields might be a usability improvement when there are a lot of Channel fields. Possible in EE?
You can create custom tabs on the publish page and choose which fields they contain. Just click the 'show toolbar' link on the upper right hand side of the publish page and you'll see these controls:
Individual fields can be hidden by clicking on the little eye icons. Tabs can be created via the Add Tab link and populated by dragging and dropping field names from the field list to the main content area. You can also remove the default tabs if they're not relevant to the content you're working with (e.g. I often delete the Categories tab).
Once you've got everything arranged as you want it select the usergroups that should see this layout (different usergroups can have different layouts assigned) and hit 'Save Layout'.
Yes, using EE's native "custom publish layouts" (accessed by clicking the "show toolbar" link in the top right of a given channel's publish screen). How well this works for you though depends on the degree of grouping you are looking for.
One option would be if you just want a bunch of related fields moved around to be in proximity to one another, you can use custom publish layout to "collect" them together in a single publish/edit screen.
If you need to segment them (like with a heading for each group or something) the closest you can get is adding tabs and moving the appropriate custom fields into each tab.
...To edit the third paragraph of Jean St-Armand's answer above for anyone else who comes along and finds this question, you could try using Red Carrot Notes both with or without EE native tabs to build on the native functionality. It's not full of features, but the one that it has works well, allowing you to color-code headings as well as position them amongst any other fields in the control panel.