To make a tree or table control scroll automatically while dragging items, be sure to wait a short time over the first or last row of the control.
Feel free to cast your vote to this Eclipse issue to get normal auto-scrolling behavior.
In input fields for files and directories when typing the file path, you will get completion hints after a (back) slash. On Unix-like systems you even can use
~/ to complete content in the home directory.
For the input field to add or edit the path of a Git remote (Remote|Add and Remote|Edit URL) you can use
../ to complete relative paths in case you've cloned a repository parallel to another.
To complete file names in the Commit Message input field of the Commit dialog, use <Ctrl>+<Space>-keystroke.
To select words or larger parts of text, you can press <Ctrl>+<W>-keystroke multiple times until you have expanded the selection as desired. To copy or cut the whole line to the clipboard, set the caret inside the line without selecting anything and press <Ctrl/Cmd>+<C>-keystroke or <Ctrl/Cmd>+<X>-keystroke.
To quickly scroll to next and previous changes, position the mouse cursor over the area between both sides ("connector") and use the scroll wheel.
In tables and tree controls you can quickly find entries by starting to type their name. With <Up>-keystroke or <Down>-keystroke you can select the previous or next matching entry, <Home>-keystroke and <End>-keystroke go to the first or last matching entry.
For all important tables, you can configure the displayed columns by right-clicking the table header and selecting the desired columns from the context menu.