Office Web Apps
Office Web Apps is a great way for anyone to access a document from almost any device at anytime. However Office Web Apps may not be able to fully replace the software version, as they are only light in their functionality. This means that Office Web Apps will not have the same feature rich facilities that users are familiar with. This may or may not be a problem for some users. The system can be combined with the software version to provide a more complete package.

Browsers
It is important to note that there may be limitations depending on the web browser you use or your clients use. Microsoft notes that it [Office 365] is fully supported by Microsoft Internet Explorer (7.x or higher) and partially supported by Mozilla Firefox (3.x or higher) and Apple Safari (3.x or higher). Other web browsers may have functionality issues.
This link details known issues with specific web browsers: http://technet.microsoft.com/en-us/library/cc263526.aspx

Operating Systems
It should be noted that Windows XP Home and XP Media Center don’t support federated identity for authentication across firms’ IT infrastructure or partner IT systems using single sign-on (SSO).

Office 365 Plans
General feature limitations could occur as Office 365 has different plan levels, at different pricing levels. Potentially this means that depending on the budget the organisation has for the system, all the desired features may not be available.

Inactivity Periods
Inactivity Periods are a good method to detect when a user’s activity stops and to then log them out of the system for security of personal data etc. Office 365 does not have this feature, and could potentailly leave data at risk of unauthorised modification or theft. Ultimately it’s the user’s responsibilty to protect their data either by logging out of the system when they move away from the PC or by locking the PC. Inactivity Periods are an extra layer of security, but not essential if users act responsibly.