To simply check row counts, you can run the following against version 7 and then 2000 and compare the results.
select o.name as "Table Name",i.rows as "Row Count"
from sysobjects o, sysindexes i
where i.id = o.id
and indid in(0,1)
order by i.rows DESC
Other than that, you should run reports from your app to compare the results/integrity of the data. I guess it depends on what the data is (is it business critical?). I've migrated multiple databases and haven't run into any issues but before migrating, we always had a game plan to verify the results.