I use yahoo as my primary email. It seems to take forever to receive an email on my new s3 on the yahoo account. I have tested it. Sometimes I get an email within a minute or 2; other times it can be a while. Anyone else have this problem?
Are you using the Yahoo mail app, or the regular Samsung email app? If it's the regular email app, did you set the Sync Schedule? In the email app's settings menu, tap on the Yahoo account, scroll down and tap on "Sync schedule, and set Peak and Off-peak schedules as needed.
I was having a similar issue with the stock email program. Switched to Kaiten, free from the Play Store. Pushing email every 1 minute. Very happy with the app. Highly recommend.