I was recently asked to assist another team in building an ASP .NET website. They already have a significant amount of code written -- I was specifically asked build a few indiv
This is definitely something you should worry about - see a related post on the importance of Disposing DataTables.
DataTables are finalizable: if you're not actively disposing them, they're hanging around much longer than Gen0 collections and killing memory.
To measure the extent of damage in your application, you can take a memory dump using WinDbg and look at the sheer number of DataTable instances (!dumpheap -stat -type System.Data.DataTable) then look at the largest data tables in memory.
This is a common pitfall in ASP.NET applications, and one that can land you in serious trouble. If you're using shared (cached) instances of DataTables, take care to note that view filters change the original instance, they don't generate a new copy.
Also make sure that queries populating the DataTables have some reasonable limit on the number of rows returned, otherwise changes to your data can suddenly baloon memory and destabilize your application pool.