I fully expect angry comments about this....
Here's how a cold fusion experiment is supposed to work, broadly. One takes an electrochemical cell containing either regular water or D2O, and as one electrode uses palladium (prepared in some meticulous way, to be discussed further below). Then one sets the electrochemical conditions such that hydrogen (or deuterium) ions are electrochemically favored to go into the palladium lattice, up to some very high loading. It's been known for decades that Pd likes to take up hydrogen, so the fact that one can do this is of no surprise. Now, while all this is going on, one carefully monitors the temperatures of the electrodes, the water, etc. The experimental claim, coarsely described, is that after some time, cells containing heavy water under these conditions begin to get hot (but not cells containing ordinary water!). Ideally one does good calorimetry and can measure the amount of energy that comes out of the cell in the form of heat, vs. the amount of energy put in in the form of integrated electrochemical current times voltage. The claim is that in some such experiments, the inferred amount of energy out is much larger than the electrical energy in. This is "excess heat".
So, what's the problem? Well, there are several issues.
1) Calorimetry can be a tricky business. This was the main criticism of the original Pons and Fleischmann work. From what I can tell, people have been much more careful about this than twenty years ago.
2) The experiments just aren't reproducible, in many senses of the term. For example, the temperature-vs-time evolutions of nominally identical cells are completely different, and all over the map. There are big fluctuations on many timescales all over the place. Sometimes the thermal output is big, sometimes it's small. This is generally swept aside by those doing the experiments, who take a wildly fluctuating response, integrate it, and claim reproducibility because the net integral ends up having the desired sign. Not the desired magnitude, just the desired sign. What would I expect to see in a well-controlled experiment? Take one large piece of palladium, cut it into thirds, and set up three identical cells. The temperature-time histories of these things should really reproduce. If you can't do that, then you don't have a controlled experiment. This isn't a small thing.
3) The cells stop working after a while. Unsurprisingly the time period varies from cell to cell. Now, why should this happen unless the underlying process is chemical in some way? By the way, some cells (but not all) "revive" when the electrochemical conditions are changed. Again, all of this is massively variable, even between nominally identical cells in the same labs.
4) The claim of excess heat assumes that there's no chemistry taking place. For example, what if I made that assumption and looked at my car engine? The amount of electrical power input by each spark plug is miniscule compared to the total power out. If I neglected chemical reactions, I'd come to the conclusion that something amazing was going on. Furthermore, if I normalized the output power by, say, the number of platinum atoms at the tips of the spark plugs, I might then conclude that the only way of achieving such power out was something like nuclear. That's the hazard of ignoring possible chemical channels. The issue here is that palladium is known to be highly catalytic, and there are certainly diffusion processes within solids that can be strongly influenced by isotopic differences. Moreover, the claim is also that surface prep of the Pd is of absolutely critical importance. Again, this sounds to me like catalysis, not a bulk effect. Now, you'd think this could all be resolved by analytical chemistry - look at the cell materials before and after running. Look at the water before and after running. However, remember that the different folks doing this disagree on basic analytical chemistry issues like the possible production of helium, tritium, etc. That has to make you wonder about how trustworty their collective analyses are.
Now, I'm not saying that there's nothing worth examining here. The DOD clearly thinks its worth looking into, and it would be nice to get this straightened out once and for all. However, 60 Minutes notwithstanding, the work is just not reproducible in the sense that most experimental physicists would use.