The Salesforce platform does not allow developers to leverage the spell check function on custom Visualforce pages, such as the New Comment page. We recommend using Firefox or Chrome which offer inline spell checking and a generally superior experience with Salesforce.
This idea addresses the platform limitation preventing us from adding a spell check button. Please vote it up!
Inline spell check add-ins are available for Internet Explorer. If you are unable to switch to another browser can google "Internet Explorer spell check" for some options.
If your organization primarily uses Google Chrome, you might consider checking out Grammarly, which is a Google Chrome grammar check extension. Please note that Grammarly only works in the Salesforce Classic Experience. E2CP's New Comment Page in Lightning uses iFrame for its text areas, and unfortunately that is not supported at this time.