Actually the first O365 tenants are updated to SharePoint 2013 backend components in the background. This results in some technical difficulties. One is the Search. The SharePoint 2013 Search Engine based on a new / upgraded Search Backend system. The FAST Engine had a big impact in all the new functions and features. More details can be found here: http://nbsharepointtalk.blogspot.de/2012/07/whats-new-within-sharepoint-2013-search.html .
If your tenant is updated to the new backend system but your frontend is still SharePoint 2010 you have some loosing. The point is that a lot of keyword calls not working anymore. For example: Path:"Posts" AND -Path:"personal" (meaning: show all which contains “Posts” but not contains “personal” in result it shows blogposts but not posts from blogs hosted in MySites). The reason is that the Managed Property “Path” no longer exists in the new Search Engine. It is replaced by ”SPSiteUrl” and so on…. Another point is, that the new Keyword Query Language and also FAST Query Language which is now supported in SharePoint 2013 cannot full functionally be used with the SharePoint 2010 UI, even the search backend is upgraded. This is because the SharePoint 2010 Webpart are not able to handle search term like author:starts-with("Nicki"). So this is a poor interims situation at the moment. But the complete update is availible soon ;-) and then we can use the full functionality of the new Search Engine.