Grant's presidency is known for being scandal plagued. This is both impressive since he served in one of the more corrupt periods of American history and inexplicable since we're used to hearing about trysts in the men's room or salacious letter to Penthouse type tales of young pages.
There were more than 10 scandals Grant's administration was implicated in.
Some of the main ones were:
The Whiskey Ring Scandal: Government agents received kickbacks for helping the liquor industry avoid millions in taxes.
I don't see a whole lot of difference between then and now, except instead of suitcases of money, certain industries such as banking, home building and firearms give billions in campaign contributions to politicians to keep them in office and in return, are allowed to do pretty much whatever they want.
Black Friday: Some businessmen and bankers conspired to corner the market on gold by buying up most of the supply in the country on the open market. They would all get rich if this plan worked, since the government was expected to buy back the government bonds it sold with gold and they held the majority of the supply.
To keep the regulators away and make sure the government didn't sell gold, they recruited Grant's idiot brother-in-law to get close to him and argue against a government sale of gold. (always the idiot brother in law in these things right?)
This doesn't seem that much worse than modern times, when many industries now exist whose lobbying dollars buy them virtual monopolies and the ability to write the very laws that regulate them (see: mining, insurance, banking).
There were many other scandals that revolved around nepotism, bribery or extortion, but again, they don't seem that much worse than what we have now.
In my opinion, the reason for all the scandals were best summed up by the following:
Grant was a George W. Bush type figure who was generally an honest man, but easily influenced by underlings that used his administration for their own selfish purposes. When it became obvious to all but him that the corruption was going on, he couldn't abandon his military code of protecting his troops and refused to acknowledge their wrongdoing (see: Donald Rumsfeld, Michael Brown)
Grant was not a career politician and was somewhat naive of the ways of Washington.
Grant was a big picture guy and focused all his efforts on the great issue of the times, the occupation of the southern states and potential war with Mexico at the expense of the housekeeping or audit functions he should have performed.
Grant had political enemies that made the Tea Party look like, well, a tea party. The south had enjoyed virtual business as usual under the Johnson administration, but Grant made it clear they actually lost the war.
All in all, I don't think that Grant was such a bad president, just that he lived in bad times. The rest of the world seemed to agree too, since after his presidency, he toured the world and everywhere was cheered by crowds as the great General and liberator of the black man.