How do I find all tables in a DB that have no explicit primary key?
Couple ways to skin this cat but this works fine in SQL Server 2005 and up, and I find it a pain free way to handle the problem -

The OBJECTPROPERTY() function can list various properties about objects - like tables. One of those properties is whether or not a table has a primary key.

OBJECTPROPERTY(object_id, tablehasprimarykey) = 0 would be a table without a primary key.

So

SELECT OBJECT_SCHEMA_NAME( object_id ) as SchemaName, name AS TableName
FROM sys.tables
WHERE OBJECTPROPERTY(object_id,'tablehasprimaryKey') = 0 
ORDER BY SchemaName, TableName ;


Should give you what you need. You can see all about the other ways to use the OBJECTPROPERTY() function in books online. This is the 2012 version of the article.