They are using it as an excuse to take down dissadents which is very dangerous for the citizens, particulary when it comes to their freedom and safety. They have taken several, over the top measures after the coup in the name of safetly and security, that are thinly vailed attempts at retaliation.
In my opinion, Erdogan is using the failed coup to block political rivals and reduce free speech. Many journalists were arrested after the coup, a sign that the country's media is being policed in favour of the state. Now that he has control of the military, Erdogan can use them for his own political interests, which is likely to negatively impact Europe, the Middle East, and the human rights of Turkey's citizens.
I'm an Obama supporter, but one of my greatest gripes about his presidency is the lack of authority he and NATO seem to have over Turkey. Erdogan is not so subtly supporting ISIS by offering them supply routes, and the entire world would be much better off if Turkey went through a regime change, forced or not.
Turkey has a history of military coups. There have been at least four since 1960. Most have been successful in their endeavors. To restore stability to the government and economy, it is necessary to detain and investigate the people involved in the most recent. The Turkish government is not intended to be military rule.