Christine,
Whilst there have been 'spikes' in criminal activity like burglaries in Honiara recently, realistically the security situation is no different to Sydney, Hong Kong or Wellington. Be aware of your surroundings, don't become complacent, don't take risks. Too often I see expats who act totally differently in foreign countries and place themselves at risk. For example, they don't think twice about drinking and driving, without thinking about the consequences. Do they know it is an offence in the Solomon Islands? In fact the police only need suspicion that you have been drinking to charge you. So you drink and drive, you hit a local, you are surrounded by 50-100 people, it is your fault - so who do you blame? Worst case scenario? Hope fully there is a flight out of the country that day ...... Security - how many expats get complacent? Some don't even lock their doors as they are in a 'compound' with guards. Would you walk around Kings Cross at 2 am in the morning without some concerns? So why expect you can do it in Honiara without any risks?
I'm not saying there aren't any risks in Honiara, but sometimes expats expect more security here than they can ever expect at 'home' where ever that is.
Yes, there are social problems, alcohol, land issues etc, which are the cause of the majority of crime and other issues, but have you been to Western Sydney, Campsie, or similar places in other major cities and felt safer?