First, a disclaimer, because I have very little practice actually making beer, but have read a ton about it, especially Mr. Beer-related stuff, since that is what kind of kicked off the obsession for me. Perhaps Yooper or someone else can validate what I'm about to say...
Anyway, it looks like you followed the Mr. Beer instructions exactly. From everything I've read, it's best not to follow those directions precisely at all. You said you bottled after 1 week in the keg fermenter, which follows the instructions, but that will result in a not great beer. You should probably keep that beer in there for 2+ weeks. 3 would be better. 4 weeks is not unheard of. This gives the yeast time to clean up after itself and remove some of the not so great flavors.
If you did use the ingredients from the kit, you probably used the booster pack. That thing is basically a bunch of sugar, which is not great for a good beer. Instead, if you do get another Mr. Beer kit sometime, you might want to try adding some dry malt extract instead, or spruce up the kit otherwise by steeping some specialty grains. Mr. Beer goes for total simplicity, but honestly, if the basic Mr. Beer kit is at a 1 on the simplicity scale, than steeping and doing dry malt extract is a 3. It's really not hard; you just have to read about it and understand what is required. Also, the basic kit ingredients, like the yeast and extract, are probably not great quality, and might be pretty old. Using old liquid malt extract is bad.
Since Mr. Beer has you bottling directly from the keg (the primary), you may be getting more yeast than you'd like. It's not a terrible idea to get a little bit of extra equipment for racking it to a bottling bucket. This will also allow you to create uniform carbonation so if you run out of the 1 liter bottles again, you don't need to worry about adjusting for bottle size. By the way, if you do plan on simply adding sugar straight to the bottles, you should probably do it by weight. Mr. Beer just says add 2.5 teaspoons or something per 1 liter bottle, but you'll get better and more uniform results if you do it by weight instead using a priming calculator.
There is a large thread in the beginner forums that talks about Mr. Beer and probably has a ton of good advice for you on why your beers don't taste great, but given the basic kit ingredients, you will probably not ever be able to get a really nice beer with that kit alone, especially following the provided instructions. I haven't even bothered making my kit yet and I'm just using the keg fermenter for Graff right now.