Do not drink the tap water and even check bottled water to make sure the cap is sealed. Be very careful what you eat. Many people get sick here. There is a Jordanian UN hospital that will treat foreigners. Local hospitals have inadequate facilities. Be healthy if you come here. Avoid uncooked food and unbottled drinks.
Practice safe sex, adult HIV/AIDS is currently 0.8%, so not an issue. But still be aware just as if you were in any country.
Watch out for bicycle riders, vehicle drivers and pedestrians. Look when crossing streets, and bike riding accidents are common. Eritrea is generally safe and you can walk about at night and anywhere in the cities and not worry about crime. There are sometimes children that aggressively beg but usually leave you alone if you are stern with them.
The official languages of Eritrea are Tigrinya, English and Arabic, with Tigrinya used for most offical purposes. Because Eritrea was an Italian colony 1890-1942/7, Italian is widely understood and spoken. In addition, people understand --and some still speak-- Amharic Amarinya, the official language of Ethiopia. English, however, will get you only so far.
Eritreans are polite, hospitable and soft-spoken but, due to the language barrier, may keep their distance from foreigners. If approached by an English speaker, try to maintain an innocent topic of conversation and use universal common sense. Avoid displaying disdain, arrogance or harsh criticism towards the country, culture, religion or politics of the country, although most will be tolerant of your "mistakes" as you are a passing foreigner. You are in a police state, don't forget it!
Do not fall prey to those willing to offer you a better exchange rate for your hard currency or some other "shady economic deal". A) They could be undercover government agents, who can land you in severe trouble with the zero-tolerance Eritrean justice system, or B) Even if they are not, you run the risk of not receiving a fair trade or getting caught by the law, which is something you must avoid at all costs in Eritrea.
It is rude to take pictures of people or their property without asking for permission. When taking pictures of public buildings beware of government buildings, especially police and military buildings. Taking pictures of these is not always illegal, but, done without permission or supervision, it can be viewed as highly suspect and can result in an uncomfortable arrest and interrogation. Ask the closest official receptionist or police for permission.
Prostitution is legal but only in licensed establishments discretely placed out of the public eye certain bars, nightclubs, hotels. Public display of romantic affection is considered immodest and overt flirting with an Eritrean is viewed by the general public as akin to prostitution or soliciting thereof and can be taken as extremely offensive if the person in question or their kin is not involved in such business.
Like in many East African and Middle Eastern countries, use of the left hand to greet, eat or hand something to someone is considered very dirty. When handing something over, using both hands is accepted and even seen as respectful, but not using the left hand alone.
Dress code is generally Western, women are not required to "cover up" or wear veils, but showing too much skin, both for men and women will earn them very little respect and women who show too much cleavage or/and wear too short a skirt/pair of shorts will be viewed as prostitutes. Eritrean or Eritrean-looking women would also be judged badly for smoking. Do not however, conflate standards of female modesty with a lack of status or official capacity for women in Eritrea. Women do drive in Eritrea - all vehicles, even military tanks, ships, planes. They also command troops and serve in all the ranks of the army and government in the same capacity as men. It is a country undergoing a post-liberation accelerated and sometimes paradoxical cultural evolution.