The thing about paralel perfect consonances is one of the old rules of traditional harmony. Of course it won't be wrong to use it nowadays because not many people compose within the borders of traditional harmony. I don't think anyone sits down to a serious composition and starts with iii-vi-ii-V-I.
Parallelism has been frowned upon since the late-renaissenance and early-baroque, mainly because of two main reasons:
1) The first polyphonic works were produced by two or three voices, which sing the melody a 5th or an 8ve higher or lower. This was called an organum. There were no countermelodies no harmonies etc. After the hundred year wars (i believe) some English composers started to use the 3rds, and this idea quickly spread in the Europe. Many composers started to use the harmonic 3rds and counterpoint and they simple tried to get away from the old organums which they called the ars antiqua. Their music was called ars nova. For distinctly separating the two, they heavily avoided paralel perfect consonances. After that, this became a tradition until Debussy.
2)The music of that period strived for simultaneous independent melodies and paralel perfect consonances didn't give that feeling because two melodies harmonised by a perfect consonances gives the same invervallic structure. But if you harmonize it with tonal 3rds, the intervallic structure will change between major and minor 3rds. This was a technique called faux-bourdon; which means false-parallelism.
However, if you double a voice with an octave (it's not common to double with a 5th) it doesn't count as parallelism, you simply do that to make that voice louder. Also, in piano writing, it might not be available to avoid them in the left hand with the chords.But these are just learned to appreciate the traditional writing, after Debussy, no one thinks about them when composing.
As for how to look out for them; it's simple actually. Look at the first chord. Locate the 5th and the octave (there might be more than one or there might not be any). Look to see if they advanced to another 5th or an octave in the following chord. When part-writing, there's an easier solution: If the two chords have a common tone, they are not adjancent in the scale. In this situation; if you keep the common tones probably there won't be a problem. If the chords are adjancent in the scale, try to use inversions. Watch out for dissonant skips.