Mull is very safe and is largely free of serious crime, and the police presence on the island is relatively sparse. Most crime on the island is of the petty variety, and indeed the locals are known to unofficially deal with "problems" themselves. Police presence increases during summer season to patrol the island's roads which are prone to accidents by inexperienced visiting drivers.
When out rambling or walking on the hills the rules are the same as on the mainland - always inform someone preferably the police or mountain rescue of your planned route and what time you are expected to return - and don't forget to inform them of your safe return. Note that mobile phone coverage on the island is extremely patchy so don't rely on it when in the remote areas of the island - Vodafone and O2 are the best of a bad bunch for reliability of reception, with the lesser networks such as T-Mobile/Virgin and Three having virtually no coverage on the island at all.
Ensure you have sufficient food, water and suitbale clothing for any walking trip - the North West of Scotland has notoriously changeable weather and inclement conditions can quickly close in from seemingly nowhere.
talk
Although Mull has a Gaelic-speaking community as with the rest of Western Scotland - everyone will speak English. Natives of the area will speak with a strong Highland or Western Isles accent which may be difficult to understand at first.