Slouken, part of the Blizzard UI team tells us how to get rid of the spam in the combat log when we zone in and out of a portal or instance.
Take a read:

How to stop frame rate lag due to refiltering when you zone:

Issue: When you zone from an instance to the outside world, the combat log goes through a massive loop, pasting every combat log message in the last 5 minutes.

Why would I want to do this fix?

· You have frame rate issues when zoning

· You have recently been in a combat sessions where there are many combat log events (e.g. raid boss encounters)

Instructions

1. Select the "Everything" tab

2. /script Blizzard_CombatLog_CurrentSettings.settings.showHistory = false

This will prevent all combat log messages from being re-filtered when you zone.

Side-Effects:

This will also prevent you from seeing old messages with the "Everything" tab.

How to Undo:

If you accidentally set this on the wrong tab, select the broken tab and type:

/script Blizzard_CombatLog_CurrentSettings.settings.showHistory = true

These settings will be saved when you logout.

Original post can be seen HERE.