You must carry your passport or identity card with you at all times at all times. Photocopies are not enough. Authorities can ask travellers to show their identification at any time. Obviously this poses a risk of theft, so if you're not the under-the-shirt money belt kind of person, you may want to reconsider.
Taking pictures of military and security installations is outlawed. Even facilities that could be perceived as a security interest in verboten: bases, government buildings, power plants, reservoirs, and so on. If you're caught snapping, police could take your camera or memory card, issue a fine, even deport you.
There are strong noise ordinance regulations. Rowdy behaviour between 10 pm and 6 am is frowned upon and could get you in a bind with the police. Bratislava is becoming a popular party destination, especially for stags. Many a tourist has been fine or jailed for being a public nuisance.
There are some peculiar zoning rules when it comes to booze. In Bratislava's Old Town, for example, it's forbidden to drink alcohol on the street. Exceptions are made in special events like seasonal markets, or on outdoor bars and cafes. Violations are punishable with fines.
Drugs: better to stay away. The penalties are severe compared to other countries. Simple possession could land you in prison for three to five years. Selling is punished with a maximum of 25 years.
If you do get arrested, the police must contact the nearest embassy or consulate of your home country. Make sure this happens by asking politely.
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