The Tools->Autocheck Spelling checkbox option is not remembered and does not apply between tabs. The fact that it is a checkbox makes it appear that the setting will be remembered and will be applicable between tabs, just like other menu options with checkboxes. The fact that it is not is a usability issue as well as an annoyance for anyone who wants Autocheck enabled by default for all documents. It also goes against other user expectations, since any other software which has a similar feature tends to remember the setting.