I saw this open tin of stuffed vine leaves in our office fridge and immediately freaked out. I'd always been told that leaving food in an opened tin risked food poisoning, and I believed that. But then I realised I'd never bothered to question why this rule applied. Time to investigate.
A certain amount of searching later, and the answer is pretty clear. Storing food in the fridge in an opened tin is a bad idea, but it's not because of botulism (at least, not directly). One major issue is that with more acidic foods such as fruit juices and tomatoes, tin and iron can leak into the food, which makes it taste unpleasant and can have health effects. The CSIRO has a good explanation:
Once cans are opened some foods, especially fruit, fruit juices, and tomato products, should be placed in a clean plastic or glass container, covered and stored in the refrigerator. When these foods are stored in the opened metal can, tin and iron will dissolve from the can walls and the food may develop a metallic taste. Food containing high concentrations of tin can cause nausea, vomiting, diarrhoea, abdominal cramps, abdominal bloating, fever or headache. These symptoms pass quickly and there seem to be no long term effects of high tin exposure. However, repackaging food once a can is opened is a good practice to adopt for all foods packaged in metal cans.
The broader problem (and the reason for that last piece of advice) is that once the tin is opened and exposed to the air, food can become dry, absorb other flavours or otherwise turn nasty. That won't make it poisonous, but it can make it unpleasant.
If you have those plastic lids which reseal tins, that problem can be avoided, though I've never used them for anything other than cat food myself. Keep it simple: if you don't use the whole tin, transfer the contents to a resealable container.