I guess I can see the argument that L might not know all of Kira's capabilities. But from his mindset, Kira is -not- 'an act of god'. In other words, killing by heart attack seems like a very powerful... yet 'mortal' ability. Perhaps even the ability to control their actions before they die could be viewed as such. It's incredible, but not beyond imagination.
Where Kira's abilities go beyond that is killing in means -beyond- heart attack. Killing by a heart attack may be a specific ability... but by heart attack, disease, car accident? Well, in theory Kira could kill someone by his ability by causing someone to have a heart attack as they drive car, thus causing a car wreck. But being able to strike someone down by more than that one means is smacking of 'acts of god'. Where this comparison does break down though is Kira's ability to kill at any time. That does resemble something beyond what he should be able to do logically, just in a 'focus ability' perspective...
Looking at Light though, I can definitely see why L's intuition is telling him this. Even in the "TV announcement" of the 1500 investigators, Light
had to challenge it. Seeing Light's behavior and mannerisms even in basic conversation would be very helpful. And it's true, no one else on the investigation team has L's insight. The next episode is out, so I'll some spoiler about L's investigation in that episode...
He couldn't really trust second-hand accounts, Light could easily manipulate the people and details would be lost. Camera equipment could be used, although they are falliable and filtered. But that still wouldn't give him the ability to get the person down there to act and respond right, and even if so it would be falliable enough that Light could see it for what it was. By showing no fear of Light, he really put Light on edge. If L died though, Watari seems smart enough to help the investigators head in the right direction. So I do think L's approach was risky, but had payoffs. It does lack the anonymity though, and it does endanger the entire thing. I wouldn't have moved so soon... but L might have been counting on unbalancing him and cracking the facade all of a sudden, which it did! L's also pretty confident that Kira hasn't the ability to kill him without his name, and L doesn't know about the 'deal'. As such, it's not nearly as risky to L as one might think... at least, by Death Note. It also makes Light even more frightened of making mistakes; overanalyzing what he's doing and stuff like I mentioned in the spoiler paragraph.
Now, if the police caught onto Kira, he could always run. But as he is the 'pampered prodigy' and extremely proud, I don't think Light even wants to consider the possibility. He needs to beat L at his own game, and so I think he's not going to be "cheap" per se. He could spread around the word of who he is, but it'd obviously have to come from Light. If Light does anything that impedes L, he could at least have the police arrest Light for impeding an official investigation! This would give them grounds to search his home and anything else as necessary, too. If Light tries to hire someone, that leaves evidence that can be traced directly, and up until now that is the one thing he has been avoiding. L doesn't know about the 'other' deaths, but it's possible if L died someone investigating more thoroughly may notice Pember was involved in that fateful bus incident, and Light was one of merely two that fit the criteria for further investigation... which would bring one of Light's biggest cards out, death by means other than heart attack. Thus, killing L isn't a good idea... even if L dies and all the investigation team, that L may not be the real L. If it was, Light may bring out others like L. Also, every time L seems to get the "upper hand" on Light, Light has to explain the situation as something that works for him in the end. Light doesn't even want to think that he might be on the ropes; both an admirable trait and a tragic flaw, you could consider. He won't give up, but he's also possibly deluding himself...
I won't say that they don't make their mistakes. We think of things differently because we have a different perspective on things. Even if we try and meet theirs, sometimes people don't see what's right in front of them; with our perspective we might just have 'our answer' and be trying to work backwards and get a better method. Then again, we just might be noticing something unnatural about the anime and our intuition tells us 'something is off'. It's not unreasonable to think someone around might have heard L's words; in the manga it's said when they are coming down from the stage. It's also not unreasonable to assume Light's power might be "growing", too...
Everyone in the series seems to make errors from time to time, it doesn't mean we are better or worse for noticing them. They are mortal men, despite any aspirations for more, and this is a situation unlike anything either of them have ever been in before. Even if they are 'good', and I can easily see that they can be quite skillful, that's different from perfection or godhood.
Even the writers, you can say, are mortal men... if you don't like their writing, you don't have to. I do, I like a lot of the undercurrents I keep on noticing, and hell, I like L.