Site Conflict between browsers

Hi there i recently completed a complete redesign of a website LockSmart 24hr Locksmith every thing was fine and i tested in ALL major browsers i.e firefox, chrome and opera until firefox released a new version and now text on my site has shifted position and looks terriable. i know its a age old theme that each browser takes the infomation and displays it in its own unique fashion bur is there not a way that DW could restrain how you design your site so as to stop these conflicts?

Just a thought....