The Dot command sets all equations to use the disconnected "dotted-line" graph style: it calculates and draws points on the graph, but doesn't connect them. In addition, this graph style is made the default, so that when a variable is deleted it will revert to this graph style. The other possible setting for this option is Connected.
Compare this to the GraphStyle( command, which puts a single equation into a specified graph style.
The Connected and Dot commands don't depend on Graphing_Mode, and will always affect all functions, even in other graphing modes. The exception to this is that sequence mode's default is always the dotted-line style, even when Connected mode is set. The Connected command will still change their graphing style, it just won't change the default they revert to.
Functions graphed using the dotted-line graph style are very strongly affected by the Xres setting (which determines how many points on a graph are chosen to be graphed). If Xres is a high setting (which means many pixels are skipped), functions in dotted-line mode will be made up of fewer points (in connected mode, this will also be the case, but because the points are connected this isn't as noticeable). You should probably set Xres to 1 if you're going to be using the dotted-line graph style -- even 2 is pushing it.