"The browser cache is full and may affect your use of Gmail ." Solution

Netizen solution:
1. Use an HTTP connection to log on to Gmail;
2. Under https, click the tool menu at the top of the IE (6.0) browser, select → advanced, deselect the check status of "do not save encrypted page disks", and restart the computer.
Google should check whether users use HTTPS connection to log on In Gmail. If HTTPS is used to log on, no error prompt will pop up. After all, the red error prompt appears every time you log on. In addition, IE is the most widely used browser after all.

Official solution:
Clear Cache
The information stored in the browser is sometimes incomplete or damaged. Deleting the browser cache or cookie usually fixes the Gmail issue.
For instructions, select your browser from the following browsers:

Firefox
In PC Firefox:
Exit the Gmail account and close all other open browser windows.
At the top of the browser, click the tool menu and select clear private data ....
Select the cookie and cache check boxes.
Click "Clear private information.

In Firefox on Mac:
Exit the Gmail account and close all other open browser windows.
Click the Firefox menu at the top of the browser and select preference...
Select the privacy tag.
Click Clear now at the bottom of the dialog box ....
In the new dialog box, select the box next to the cache and cookie.
Click "Clear private information.
Internet Explorer

In Internet Explorer 6.x:
Exit the Gmail account. Close all other open browser windows.
Click the tool menu at the top of the browser and select the Internet option.
Click the regular tab at the top of the dialog box.
Click Delete file under Temporary Internet Files ....
Select the box next to deleting all offline content.
Click OK.

In Internet Explorer 7:
Exit the Gmail account and close all other open browser windows.
Click Tools> Internet Options.
Select a regular tag.
Click Delete under browsing history.
Click Delete file under Temporary Internet Files.
Click Delete cookie.
Click OK.
Mozilla

In Mozilla:
Exit the Gmail account. Close all other open browser windows.
Click the edit menu at the top of the browser and select preference.
Click the plus sign next to "advanced.
Click cache under "advanced.
Click Clear cache.
Click OK.
Netscape

In Netscape:
Exit the Gmail account. Close all other open browser windows.
Click the edit menu at the top of the browser and select preference.
Click the plus sign next to "advanced.
Click cache under "advanced.
Click Clear cache.
Click OK.
Safari

In Safari:
Exit the Gmail account. Close all other open browser windows.
Open the safari menu in the browser toolbar.
Select clear cache.
In the dialog box, Click Clear.
Other browsers

Sorry, Gmail does not fully support other browsers, and other browsers may be incompatible with some Gmail functions.
In some cases, you may need to clear the cache multiple times.