Will the average tourist encounter problems on the street in Cape Town?

To keep it less subjective, I wanted to give an answer that mentions an existing numerical index based on data.

Numbeo lists its safety index for mid-2015 at 29.64. You may want to compare it with other cities that you have visited. For instance, since your profile mentions UK, Buenos Aires and Tel Aviv:

• Tel Aviv 66.86
• London 51.83
• Buenos Aires 37.43
• Cape Town 29.64
• Memphis, USA 28.12
• Rio De Janeiro 25.80 (I know, it isn't in Argentina, I was just looking for a big city rated lower than CT)

Overall it's quite low on the list. That said, I have been (and I looked quite tourist-y) in Cape Town and another city rated lower, and nothing happened to me.

(Warning: Numbeo is a big time sink.)

The tourist attractions and the Cape Town city bowl are usually very safe. The local government is making a lot of effort to deploy city police at these attractions. It is one of the only cities in South Africa where it is safe to walk around in the inner city. There are buses serving all the tourist attractions, and a bus network serving other areas, but not as elaborate as Europe. There is also Uber taxi's which serve's Cape Town quite well. If going to Wine farms, Uber would probably be your best bet as there is no public transport to the Wine farm regions.

It is, however, very strongly advised not to go into the informal settlements, unless coordinated by a reputable guide. But you need not be too concerned as you won't find yourself at those locations "by accident".

Using trains can be an issue. I employ quite a few people in the Cape Town area and they stick to the taxis and avoid trains when commuting, especially on Fridays.

No. From this source, Cape Town attracts millions of tourists on an annual basis. From the SA police and here, the number of contact crimes annually is of the order of 10 000. It is hard to qualify the split, but the vast majority of these violent crimes are in the townships / ghettos and on the Cape Flats, and the victims are local. These areas are highly impoverished and struggle with gangs and drugs. In tourist areas, your chance of running into trouble is extremely small. Of course, being aware is important, but the vast, vast majority of tourists have no problems.

I am South African and lived in Cape Town for 5 years without incident. I would recommend a car as the public transport is not as extensive or accessible as you would except coming from the UK/ Europe. From my experience, you would not believe how many tourists ignore all safety advice and common sense - wandering round at night, flashy jewelry etc - and get away with it. This is not recommended though!

I will also add this link which supports that the average tourist will not have any problems.