Shameful acts, let's see. Arguably the worst act done by the Turkish Government, is Wealth Tax (Varlık Vergisi) that was levied on the wealthier citizens of Turkey during WW2. This tax was simply to fund the army in case of an invasion by either the Axis or the Soviet forces. However, the arbitrous officials targeted mostly the non-Muslim citizens. They raised the tax so high, that after families couldn't pay, they were either sent to prisons or to a forced labour camp in Erzurum. 21 of our citizens died there. On top of that, 320 million Turkish liras (approximately 276 million American dollars) worth of assets were taken from them. Nearly half of the non-Muslim community left the country for another.
The worst act done by the Turkish people is, in my opinion, 6-7 September Incidents in 1955. Turkish newspapers showed the news of the bombing of the birthplace of Atatürk in Thessaloniki, Greece. The Turks assumed it was done by the Greeks, however, it is later found that it was orchestrated by some Turkish guy who later got arrested and confessed. (The bomb was found a day ago before the news arose)
This incited a big mob in Istanbul led a terrible riot, which included arson, raiding, looting and beatings in anywhere. It wasn't directed at anyone at first, but later on the most affected ones were citizens of Greek, Jew and Armenian descent. More than 10 thousand properties, %40 of them were owned by Greeks, were damages, and around 30 non-Muslim citizens died. After that, nearly the entire Greek population and a great deal of Armenian and Jew population emigrated from Turkey. On top of that, the guy who incited these events later on was allowed to finish his studies of Law in Istanbul University, and went on to become the governers of important districts, one of them being Beyoğlu, in which mostly Greeks inhabited once. This marked the day that Turkification (by that, I mean Muslimization) of assets in Turkey and of the population, was almost complete.
In addition, assuming only we're regarded as the continuation of the Ottoman Empire, the acts that were done by Hamidiye Regiment and CUP against the forced emigration of the Armenians are most saddening as well.