Editing the template jungle of a main page is not exactly something VisualEditor is reasonable to use for, so I am mainly filing this in the hope that it uncovers a more generic bug.
The main page of hu.wikipedia is relatively straightforward: a table with two columns, each cell containing the "mainpage section" template which transcludes some other page which has the content, and adds borders and other styling. Trying to edit the "mainpage section" templates with VE fails on both FF and Chrome (did not test others), in different ways.
On FF (44.0.2/Win), clicking on a table cell selects all the text on the page and scrolls to the bottom of the page. See video by @Samat. Sometimes clicking on a cell highlights the cell in blue and brings up the table cell dialog, but most of the time it just does the select-and-scroll thing (it seems completely random).
On Chrome (48/Ubuntu), clicking on table cells highlights them in blue, but does not bring up the table cell dialog, and there is no obvious way to interact with the contents of the cell. (Pressing a cursor key does it, but that's hard to figure out. I would expect a popup dialog, or at least doubleclick to move the cursor inside the cell.