Hi Erik, welcome to the forum... it has been really helpful to me and I hope it will be for you, too. You will probably get a lot of help on this subject.
I've owned the 510 since before Christmas (Yes, there is a Santa!), with both kit lenses and my experience is that it has to be awfully dark before you can't auto focus.
Even then if you select one AF sensor (I use the centre sensor almost exclusively), you can usually find something to focus on. My favourite target is the eye because it's most reflective on most faces, unless heavily shaded, and if the eye is in focus the face will look sharp. Next best is a cheek bone.
Hone your trigger finger reflex and be ready; when trying to focus on something difficult, the focus will jump around a lot. That's a problem, of course, but the lenses and the AF are so quick they will usually lock on at some point. Be ready, and be quick, and you'll be pleasantly surprised a lot of the time. If not, well there's always delete.
I'm not really fond of the flash-based focus assist; it doesn't seem to be that consistent and it's pretty intrusive unless the party is really happening.
One trick is to use your 14 to 42 lens more than the longer lens, get close and don't use it at the longest end; lens aperture is vital to AF, it's all about light getting to the sensor.
Would also suggest practice with the manual focus before it counts. Try to duplicate the lighting conditions and levels and locate moving targets... our cat has become my target of opportunity. If I can make her nervous enough she will pace at a slow walk for people.
Then I shoot a bunch of photos at medium resolution jpeg settings and upload them to the laptop for the acid test. You'll be pleasantly surprised.
Now, it's off the topic of focusing, but while practicing with your focus, use the opportunity to experiment with flash modes. The most obvious mode to try is fill flash; that offers the excellent exposure meter in this camera a chance to help out. It can produce some really natural but super clear photos with less flash shadow than normal.
For even more natural views, albeit with some penalties (if you want to call them that… I like a bit of motion blur. It ads some dynamics that borders on video effects when everything works right!), try your slow synch. When everything comes together, you basically have a photo taken by ambient light with the flash providing some key highlights for a nice bright look that is exceptionally natural and pleasant.
Depending on what you need the photos for, don't be afraid to go to ISO 400 or 800, to provide shutter speeds of no more than 1/4 second. Speeds of 1/18 to 1/15 are safer and 1/30 second will eliminate blur with most people chatting and standing around. The slower shutter speeds will provide some blur if people nod or turn their head or wave or step quickly. If you have to key on a particular person study him or her while shooting a few photos and look for when there is no motion or very little. Again quick reflexes are a saving grace.
This is where the beauty of IS comes in; like with video, a good image begins with a still, or stabilized, camera. No matter how interesting your subject is you will have only abstract art if the movement isn't against a stable background. IS will hold the background solid down to some truly dangerous shutter speeds. But that can provide some absolutely amazing people photos if you give it a chance.
One final "However"… photojournalists live and die by one cardinal rule: it's OK to play, but first make sure you have one good, solid photo in the can. It might not be the most exciting or dramatic but it will have the subject in focus, well exposed and fill the hole your editor has. Once you're safe you can experiment, but not before. As one dear editor once told me, "We don't publish our mistakes or anything that looks like a mistake."
Trust your 510 and it will pleasantly surprise you, time after time!