Shortcut Key to Edit Cell in Google Sheets

Use the down arrow to select the auto complete you want then press TAB.

This will populate the search box with the selected auto complete item, add a space and position the cursor after the space without executing the search. You can then continue to add search terms, using the down arrow and TAB where more auto complete suggestions are applicable.

Only when you've finished with your search terms, hit ENTER.

Per the official list of keyboard shortcuts, F2 is the only key responsible for editing a cell. I've just tried it in 3 browsers (Chrome 16, Firefox 9, and IE 9) and it doesn't function the same way as it does in Excel.

Your solutions are 1) pressing F2 before entering any data, 2) pressing Backspace to remove the characters you've typed after the error, or 3) using the mouse to navigate.