If "Check spelling as you type" is not working for checking the misspelled words on table then you need to follow the steps mentioned below to make it do so:
1. Firstly you need to open your document and select the whole text by pressing on Ctrl + A.
2. Then you need to Go to the Review-then select Proofing- Then set the Language (Word 2007).
3. Then you need to Go to Review- then Language- Then Set Proofing Language (Word 2010).
4. Then you need to Uncheck the 'Do not check spelling or Grammar' option.
5. Then you need to Click Ok and again check your document.
If still the spell checker is working or not work then there can be many reasons that can lead to this problem such as restrictions of add-ins or due corruption with the word files. To solve these issues you can make use of the third party repair tool-MS Word File Repair Tool. It is an efficient and easy to use tool that helps you to resolves all the issues related to MS Word File.
For More Information:
http://msword.filerepairtool.net/blo...er-working-fix