I've had some spotting too, Hooplehead, and have consulted extensively with my OB and my aunt, who's a nurse.
You don't say how much "some" is, but what I've been told is that if you're not spotting a lot and you continue to not spot a lot, it's probably not a big worry. For example, I've been spotting, but it's only ever been when I wipe--I haven't needed a pantyliner, and the spotting hasn't increased, and I'm told that this probably isn't something I need to be concerned about. Pink or brown blood is better, from a pregnancy-maintenance standpoint, than red is.
A handful of potential non-big-deal reasons that you could be bleeding: cervical polyps, bursting a blood vessel in your cervix while bearing down to poop, hormonal changes around when you'd normally have your period, and cervical irritation or infection. My OB claimed that between 30 and 50 percent of women have some spotting in their first trimester; my aunt said 30%; the internet says 25%. Either way, that's definitely not an insignificant number--and the vast majority of those people go on to have healthy pregnancies. So don't lose hope yet!
If the flow gets heavier, you start having severe cramps, you're having shoulder pain, or you start to run a fever, you should get in to your doctor or the emergency room ASAP--those symptoms could be indicative of miscarriage or ectopic pregnancy. And, really, it couldn't hurt to phone your care provider now and just say "Hey, this is happening, is there anything I should be doing?" Most likely they'll tell you no, but if it'll set your mind at rest, I'd definitely give them a ring.