First you have to know that the universe of securities cannot be correlated all the time except in time of crisis where correlation becomes very high. So we have established that securities are uncorrelated now. so what could go wrong here ( why are they correlated over time ) :
I- correlation is based on the covariance and variance of securities ( which is collected from past data) and the larger the sample of data ( i.e. the more you go back in time and collect data ) the better your correlation results. so when you have faulty data, it is possible that your correlation measures might end up positively skewed and not very representative. Also collecting data from different markets might also produce innacurate results.
III- Again correlation is based on past performance, so when market are weak form inefficient that means they could be exploited for abnormal profits using technical analysis which is based on past data.