The Project 2010 SDK includes a general discussion about updating applications developed for Project Server 2007 to run with Project Server 2010. Because the PSI in Project Server 2010 is a superset of the previous PSI, many ASMX-based applications can run unchanged on a Project Server that uses only Windows authentication -- but all require testing before deployment on Project Server 2010!
The Project Server Programmability page includes the Porting Applications Built for Project Server 2007 section, which links to the Migration and Compatibility of Custom Solutions section in the Overview of WCF and the PSI. In addition to the information on those pages, applications for multi-authentication installations of Project Server 2010 must be updated to handle forms-based and Windows-based authentication in the Claims environment of SharePoint Server.
The ASMXLogon_MultiAuth sample in the recent Code samples from the Project 2010 SDK webcast blog post provides an example, using the information in the Using Claims Multi-Authentication discussion in the Prerequisites for ASMX-Based Code Samples article of the SDK.
Even if your older application works on Project Server 2010, and you use only Windows authentication, it is a good idea to update the web service (ASMX) references and recompile, as described in Migration and Compatibility of Custom Solutions .