There are unlikely to be issues, especially if you are not doing anything much fancy SQL-wise, but this is not guaranteed so I would be inclined to test against SQL2008 to be sure - if only on express edition (which won't cost you).
If you don't retest on 2008, at least ensure that all new databases have the 2005 compatibility level (90 - see here for more info). Compatibility level doesn't guarantee complete issue free running though if you your code (intentionally or accidentally) depends upon any "undefined" behavior that has always been the same in SQL2005 (and perhaps prior) by chance.
Regarding "the host says that there should be no changes to be made": the host is unlike to be a SQL expert, they are a hosting company not advanced DBAs or developers - the most they can legitimately say with any guarantee (IMO) is "we've had clients upgrade to 2008 and they have not had any problems that they reported to us". It also would not be in their interests to say anything like "yeah, you might have to test to ensure no problems with SQL2008" if 2008 is all that they offer...