There are good points with Sharia, Moslems frequently point out that Widows and orphans should be looed after for example. Unfortunately there are many areas where decent civilized people will disagree with Islamic rules. Liberal Muslims overlook the worst aspects of Muslim law in the same way that Liberal Christians overlook the worst parts of the Bible.
Problems with Muslim Sharia Law
Sharia allows slavery. Mohammed himself owned 40 unfortunate slaves. Slaves are helpless before their masters, can be bought and sold and masters can have sex with female slaves whenever they want.
For more about abuses suffered by slaves under Islam, see the following:
Wives may be beaten simply for being too independent and not respectful enough.
People may be severely flogged for drinking or gambling
Of course, don't expect any men to be flogged. Even though President Anni drank Sula shiraz, the courts failed to look into the case and have him flogged. If you look at Maldives law, any man or woman who is proven to drink alcohol has to be flogged.
People who have blinded someone else may be blinded themselves
This has actually happened in the 21st Century, see the following:
Thieves should have their hands amputated
The Koran stipulates this, see the following:
Crucifixion and other forms of torture are allowed to punish some crimes
Laws allowing crucifixion and other barbaric punishments in Hamas controlled territories have been passed. There have been several crucifixions in Saudi Arabia during the last 20 years and at least one innocent man was lucky to escape crucifixion in Saudi Arabia.
Homosexuals are punished by death, by severe flogging or by long prison sentences
Traditionally homosexuals were sometimes burnt alive but as recently as the 21st Century in Taliban controlled Afghanistan were routinely executed. Lucky ones were thrown from tall buildings and died relatively quickly though it must have been terrifying. Unlucky homosexuals were put into a pit and a wall was toppled onto them so they were buried alive. In Iran women caught doing lesbian acts were/are given a hundred lashes each but if they have not “reformed after three such punishments they are executed the fourth time.
See the following:
Heteroxexual sex outside marriage
Unmarried people of either sex who have intercourse should be whipped and given a hundred lashes, this severely lashing can be fatal. Adultery is punished even worse, male adulterers are hanged while female adulterers are buried in a pit up to their heads and stoned to death. A case is pending or was pending when one of my sources was written where a woman in Iran faces being stoned to death while her male partner risks being hanged both within a month and Amnesty International is asking people to write to the Iranian authorities over this. 
A recently as 2008 a 13 year old girl was gang raped and later stoned to death for fornication. The unfortunate girl screamed and begged for mercy and relatives tried to help her, then Muslims started shooting causing a baby’s death. In Bangladesh rape victims are commonly flogged or beaten while in Pakistan rape victims get long prison sentences.
See the following:
This article is work in progress, there’s much more to write.