I can't say that there are any unique dangers that are specific to Cleveland. One should use general precautions, as you would in any 'big city.' But I think, for the most part, Cleveland is pretty safe. I did find myself stranded in a seedier part of downtown once, and that wasn't the best feeling in the world, but the police were patrolling fairly frequently, and I made it home in one piece!
This controversial ban was voted into effect in November of this year (2006) and requires that public work places and other public places be free of cigarette smoke. If you're a smoker, where you can smoke is greatly limited. If you're not a smoker, it will be easier to enjoy going to bars, cubs and restaurants, amongst other public places, and will ultimately be better for your health by limiting your exposure to second-hand smoke. I encourage you follow the link below for more information and clarification of any confusion, and where smokers can smoke.
If you are on I-71, be careful for the village of Linndale (pop. 117). It is between exits 244 and 242 on I-71. Although Linndale does not have an exit itself, a 500ft stretch of the highway's geography runs through the city. It is a notorious speed trap, and there is ALWAYS a Linndale officer watching on side of the highway. Even violations for only +5 mph over the speed limit will be cited; the village raked in over $1.2million in tickets in 2005 alone and the questionable practice is always being scutinized by local media, lawmakers, etc. Please drive the speed limit on this section of road.
If you're going to be in Cleveland soon, you'll probably encounter a major construction project downtown, the Euclid Corridor Project. It's a messy project that could've been better planned, and updates as to what areas are currently torn can be found here:
Watch out after a game at night tons of people head out onto the streets all at once..Some people forget how to drive after they have had a few. The Rock and Roll hall of Fame, waterfront and Great Lakes Science Center are near here making this a very congested place at times.
In the 80's, urban flight left downtown Cleveland in trouble. The town has done much towards rebuilding the area such as with a relatively new baseball stadium and warehouse district with restaurants and bars. Nonetheless, there is still remnants of urban problems and so there are homeless and the like downtown. I guess every city has this to some extent. Tower City seems to attract all sorts and so be mindful not to stray too far from your destinations.
Driving in Cleveland is a drag as main roads often have a speed limit of 35 miles per hour with some areas changing to 25 miles per hour. One road, Mayfield, runs from Case Western to the suburbs and has such changes (i.e. speed traps). This is par for the course in old cleveland. One needs to pay attention to the posted speed limits. Also, in some places there are traffic lights every 1/8th of a mile so sometimes its slow going. (Hm. It's said Cleveland's economy is sluggish - wonder if it has anything to do with their outdated traffic system!!!)
The only neighborhoods considered dangerous are those tourists have no reason to visit. There are many panhandlers downtown, but they are harmless. Enjoy your stay in Cleveland! :)