OK Arlene, while I certainly empathize with you [more than you may know] let me play Judge Judy with you. You will not like me if you have never watched that show but here goes;

First, they dug up part of the stone driveway in front and put in a veggie garden.

That would be considered natural and organic by many and I would expect no relief.

It looks neat now but I know at the end of the season all of the dead plants and veggies will lay there and not been cleaned up.

OK, here comes the judge. It makes no difference what you "think" will happen when it comes to enforcing codes. If it does become a health hazard in the Fall then you have a shot.  

There are seven bikes laying (and I mean thrown) in front of the house, where there is a fenced yard where they can be kept.

There is no code I know of preventing this. Being "thrown" or placed is irrelevant. This goes to neatness which I think you will find difficult to enforce.

There are Eagle flags (last I counted six) hanging there since October. Some are hanging off.

No ordinance that I know of preventing this either.

The leaves are not cleaned up. They did clean up debris that was piled three feet high when I called but not the leaves. Last October they cleaned the roof off (first time in three years) and all of the leaves from that are laying in a pile, which now has weeds growing out of the pile.

I have been down this road in the past. If leaves are just left lying in the yard there is little that can be done HOWEVER you may have a shot here. If leaves are raked into a pile as you indicate that is a definite violation and OPA can come in if the neighbor refuses to pick them up, clean them up and bill the homeowner. Have you notified OPA?

Private property pigs as I call them are tough to deal with due to private property rights. I wish there was more that could be done as these type properties are a blight on the neighborhood and do nothing for our property values in the Pines. It is also interesting that the home is a rental. One would think the homeowner would take a little more pride in his community instead of becoming a slum landlord.