Statins are like all medications - they have potential risks and benefits and shouldn't be used by anyone when that ratio is unfavorable.
Memory problems including "transient global amnesia" have been reported for years and may not be more common than with placebo. There is no convincing evidence. Does that mean it doesn't occur? Of course not, just that is may be coincidental or idiosyncratic or very uncommon.
Sexual dysfunction: same can be said.
Liver and muscle dysfunction or inflammation: yes, occasionally. Usually reversible if stopped early.
OTOH, in patients who are well selected, the annual risk of heart attack or sudden death is in the range of 1 to 7% per year, depending on all the risk factors. It is lowest for people who are otherwise healthy but have incidental adverse cholesterol profiles, highest for those with a prior heart attack, diabetes, etc. Taking statins reduces that risk by 20-40%, which corresponds to an annual absolute risk reduction of say .4% to 3%. This is annual and cumulative. These benefits are generally much higher than the risks in question for properly selected people.
Home cholesterol monitoring is probably little value. It generates more anxiety than help for many. Even in high risk patients, we check every 6 to 12 months at most. The home machines are of uncertain reliability. The best single predictors are the total:HDL ratio (in the context of appropriate LDL elevations) or - even better - the nonHDL choleseterol which is Total Chol minus the HDL chol. These results are interpreted in the context of family history, other risks, age, gender and so forth. In this way you can determine for whom taking a statin is a sound bet, versus a waste of money.
Finally, there is decent evidence to show a drop in stroke rates from statins, and also suggestive but unproven data about reductions in the incidence of Alzheimers. The jury is still out on the latter.
In any event, lifestyle modification and weight control should always come first. Statins are best reserved for those whose abnormalities persist despite these (occasional) or whose lifestyle efforts and goals are not met long term.
Hope that's helpful.