Generally, it is safe to walk around in this district, even by night, though crossing the TarlabaÅı Boulevard TarlabaÅı Bulvarı towards the dilapidated quarter of TarlabaÅı to the west of BeyoÄlu/Istiklal Avenue wouldn't certainly be wise after the night falls. Some other parts of this district also have some crime issues. A rule of thumb to follow would be to look for young people around having fun, which suggests that you are more likely in an OK zone.
Taksim Square and Istiklal Street there are always 7/24 police officers and security cameras. Do not be afraid. This is a safe area.
This part of the city is where much of the bar scams take place. These scams are explained in dedicated section of main Istanbul article in detail.