Effects on inference: positive autocorrelation makes observations less informative than they appear, so effective sample size is smaller than n and standard errors computed naively are far too small.
In returns: typically very weak at short horizons - which is roughly what market efficiency predicts. But squared or absolute returns are strongly autocorrelated, which is volatility clustering.
The Sharpe warning. Positive autocorrelation inflates a naively annualised Sharpe ratio, which is one route by which reported figures overstate performance, especially for illiquid strategies with smoothed marks.