@fael, I have problems with both of your sentences, mainly because they are ambiguous. I am not sure if you mean, 'Those who are in power can monitor communications and they can also track down opponents', or, 'Those who are in power can monitor communications so that they can track down opponents'.
If you mean the former it would be better to include the phrase 'track down opponents' first, so that it does not get confused with the remainder of your sentence, eg:
Additionally, those who are in power can track down opponents and monitor communications for specific opinions, particularly political attitudes.
If you mean the latter then 'track down' needs to be changed to 'to track down' or 'tracking down'. The preposition 'for' in the prepositional phrase 'for specific opinions' will be carried through to the phrase 'track down'. However, in English we do not say 'for track down', the correct phrase is 'to track down', if you wish to retain 'for' then the phrase could be changed to 'tracking down opponents'. This would then change the sentence to either:
Additionally, those who are in power can monitor communications for specific opinions, particularly political attitudes, and to track down opponents.
Additionally, those who are in power can monitor communications for specific opinions, particularly political attitudes, and tracking down opponents.
I also agree with Jeff Morrow that matching 'specifically' (or 'specific') with 'particularly' and 'opinion' and 'attitude' tends to muddy your intended message. "Specifically' means 'to be exact, clear or precise'. In particular 'opinions' should not be conflated with 'attitudes'. "Attitudes are assumed to be more affective than cognitive, whereas opinions are more cognitive than affective." (Attitudes, Opinions and Why Dinner Matters). In other words, attitudes are based on what we feel and opinions are based on what we think. It should be noted that attitudes can influence opinions, but opinions are less likely to influence attitudes.
Taking all of this into consideration, I would suggest that you might say:
Additionally, those who are in power can monitor communications [specifically] for [specific] opinions (eg political opinions) and to track down opponents.
In the context of this sentence it does not matter if you use 'specifically' or 'specific'