Flowers, what herb and oil did you use? Some herbs need to be dried before infusing, some are best used fresh. It is really important that your equipment is very clean when you start. Jars should be sent through the dishwasher, if you have one. If not, scald them with hot water. Then, make sure they are completely dry before adding herbs and oil. I use high quality olive oil for most of my infused oils. You can use a crockpot to heat oil and herbs, you can solar infuse, you can cold infuse. Again, check my response to your tincture question for two great books. Also, give specific as to which herb/oil combo molded on you and I'll try to help.

That is a REAL problem... and is supposedly why you shouldn't give gifts like Basil infused olive oil..basil has some kind of fungus that lives on it... that will go crazy in the oil.

Well I was thinking of calendula oil because I've never heard it used in a tincture.... and I was going to use it topically..... :)

calendula oil is one of the easier ones... you might throw in a chamomile flower or two...chamomile is an anti-fungal.

Calendula must be absolultely dried to make the oil. It is rather resinous, so can take a long time to dry. To expedite things, instead of using the entire flower with the calyx, pluck off the petals and dry those. The petals dry quickly.

Is it true that fattier oils (like olive or macadamia) produce better infused oil (better constitutent extracting qualities) than lighter oils? :)

I would recommend only using particular oils. Some oils will go rancid before others. Jojoba oil is the best, as it almost never goes rancid. I have also heard people recommend Seasame oil for the same reason. Just avoid using Olive oil as it will go "bad" faster then any of the other oils.

Can I use grapeseed oil or sweet almond oil to make the oils?

I would think Almond oil would be fine, I would have to look it up to check. Grapeseed oil actually has disinfecting qualities so I would expect it would not go rancid either. Which you want to use would probably depend on what you are wanting to use the finished oil for. Some oils are recommended for skin (jojoba) and others are recommended for hair etc.

Are you planning on using the infused oil internally, externally or both. I add a few drops of benzoin tincture to infused oils I use externally and none of them have ever gone bad. Good luck.

I use 16 oz jars and fill a little more than half way with herb/plant and pour olive oil over it. I make sure there are no air bubbles or exposed plant. Screw lid on tight and sit in the sun for 3--4 weeks and after store in a cool dry place...fridge fine. People have trouble when they often leave in air bubbles or they don't chop and cut plants with stems (stems have air in them)

I like the idea of using Jojoba oil. Could one use Meadowfoam Seed Oil or Coconut Oil?

Also, if making a rosemary oil, would you suggest the herb be fresh or dried?

I slightly dry the plant before hand if it's particularly mucilaginous (like plantain), but mostly use fresh plants; with them, I fill up a jar and cover them with olive oil and make sure there are no air bubbles. Then I leave it out in the sun for a month or so, and strain... it really helps if you add in a few drops of Vitamin E oil, that prevents the base oil from going rancid (it has so far, anyway).

Some of the people's recommendations are VERY DANGEROUS. Contact your nearest Land Grant University Extension professional (usually called Extension Agents, Extension Educators, or Speciailists) for information or check out:
http://www.foodsafety.gov/poisoning/causes/bacteriaviruses/botulism.html
herb infused oils can promote botulism growth because the oil coating of the herb can create an anaerobic (without oxygen) environment

Here is a link that might be useful: USDA Food Safety