- They actually had more soldiers than was shown on TV.
is correct. The singular "was" is used because reference is being made to the fact that they had more soldiers, or to their having more soldiers, which are singular subjects. The plural "were" is also possible as stated by Edwin Ashworth in his comment, the only slight difference being, in my opinion, that "were" seems to emphasize the individuality of the soldiers, while "was" points to the group as a whole.
Your question, however, revolves around the use of a verb after "than", without a pronoun. Actually, it would be incorrect to use a pronoun. Something similar occurs with "as":
- They actually had a lot of soldiers, as (was) shown on TV. (With "as" the verb "was" will tend to be omitted at all times.)
On this page you will find both "than" and "as" used as if they were pronouns (I think they are, as I once claimed in another thread that aroused some controversy), without another pronoun after them:
As and than can introduce clauses in which there is no subject or object pronoun. In this case, they act like relative pronouns.
The meeting was as successful as had been expected. (NOT The meeting was as successful as it had been expected.)
You worry more than is good for you. (NOT You worry more than it is good for you.)