Most professional observers believe that despite the increasing popularity of new, digital information sources,
the financial success (subject) of the weekly magazine–or at least some of the weekly magazines–seem secure for some time to come.
A. that despite the increasing popularity of new, digital information sources,
the financial success of the weekly magazine–or at least some of the weekly magazines–
seem (SVA error) secure for some time to come
Success is singular and needs a singular verb.
B. that, despite the increasing popularity of new, digital information sources, the financial success of the weekly magazine–or at least some of
them–
seems secure for some time to come
C. that, despite the increasing popularity of new, digital information sources, the financial success of the weekly magazine–or at least some of the weekly magazines–
seems secure for some time to come
The only difference between B and C is the use of them. GMAT always prefers to repeat the noun and to make the sentence as clear as possible. Also in Option B - them (plural) cannot refer to the magazine (singular) so it will refer to sources which is incorrect. C eliminates this error by saying weekly magazines.
D. that the financial success of the weekly magazine–or at least some of the weekly magazines–seems secure for some time to come,
this is despite the increasing popularity of new, digital information sources - misplaced modifier error. Construction is much better in B and C.
E. that the financial success of the weekly magazine–or at least some of the weekly magazines–
seemed secure for some time to come, despite the increasing popularity of new, digital information sources
Option E: changes the verb from seem to seemed. This sentence is making a prediction about the future, so using the past tense seemed is incorrect. You need to use the present tense seems.