Does this affect all sites, or only links that open in a new/popup window?

If you use your Firefox desktop/QuickLaunch icon to start a new Firefox window, does it have a scroll bar?

Do you use automatic private browsing mode, which generally is set in the Options dialog, Privacy panel, as "Firefox will: Never remember history"? A user with that setting reported getting limited feature windows in that mode and I wonder whether it is a pattern.

Ref: Private Browsing issues: New window is a "pop-up" & Right-clicking bookmarks shows grayed-out options (unsolved)

You can try to rename (or delete) the xulstore.json file in the Firefox profile folder.

You can use this button to go to the currently used Firefox profile folder:

• Help > Troubleshooting Information > Profile Directory: Show Folder (Linux: Open Directory; Mac: Show in Finder)
• http://kb.mozillazine.org/Profile_folder_-_Firefox

If you have a three button mouse, clicking the middle button will turn the mouse into a scroll controller.

Based on another thread where the user tested a bunch of things, there appears to be a bug in Firefox 38.0.1 involving this set of circumstances:

(1) Tabbed browsing turned off (2) Private window (3) Link with target="_blank" (not a scripted link)

The new window opens without menus, toolbars, scroll bars, etc.

Currently known workarounds:

(1) Use tabbed browsing (2) Shift+click links to open in a new window with the standard features