This article is work in progress, there’s much more to write.
Sharia law is based upon the Qur'an and the ahadith; being extrapolated upon where required by Fiqh - which is Islamic jurisprudence. The extrapolations may vary depending on the sect and the school of thought followed by different scholars, however the core laws of Sharia remain the same across the different schools of fiqh and the sects.
There are some good laws contained within Sharia law that Muslims frequently point to, in order to show that Allah's law is superior to any other (man-made) laws; for example. Unfortunately there are many areas that are not compatible with life in the 21st century. Liberal Muslims overlook the harsher parts of Sharia in the same way that Liberal Christians overlook the more uncomfortable parts of the Bible.
Flogging is the prescribed punishmnent for many breaches of Sharia law. Below is a video of a woman being publicly flogged more than twelve times although many floggings are much worse. This unfortunate woman could get up in a controlled way afterwards which would not have been possible after a worse flogging. There is a warning that some viewers may find the video disturbing.
Most Pakistani Muslims are far less extreme than those responsible for the flogging shown above. The video below shows brief clips of the disdturbing flogging but mainly deals with Pakistani reaction.
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 on any occasion her husband fears she may do something that would displease him. This ruling of Sharia is based on An Nisa 34 (Quran 4:34). There have been cases where Muslim men have beaten their wives for being too independent or 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:
Heterosexual 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 adultery. This is because rape was not a crime in Muhammad's time (indeed, he and his companions comitted it regularly), so the jurists have had to adapt the ruling to prove adultery - which is 4 male witnesses - and have ruled that 4 male witnesses must be presented in court to prove rape.
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: