Can fair comparisons between products be made when there are uncertainties in the data?

Yes they can. But there are some caveats. 
There are uncertainties regarding several aspects in the calculations. Most of the uncertainties relate to biological processes such as nitrous oxide emissions from agricultural fields, or methane emissions from livestock. These emissions may differ depending on growing conditions, weather, differences between individual animals in a given population etc. As a food producer you typically cannot control or even know exactly what the weather was like where grains were grown, or which animal in a stock that ended up in which package etc. What can be known, however, is what the emissions are on average for different production systems. 

Different products and different production systems may thus have predictable differences between their expected emissions. With similar uncertainties, there can thus still be a point in comparing them, as long as the method for the calculations, scope, all system boundaries, and assumptions are consistent. 
As an example, say that you have two products with emissions of 0.66 kg CO2e and 0.74 kg CO2e respectively. There may be an uncertainty interval of say ± 0.08 kg CO2e for both. But the first may still cause reliably lower emissions due to known factors, i.e. factors with much lower uncertainty, such as transport or energy related emissions. Also, the producers may make an investment that reliably reduces the emissions for the second product by eg. 0.06 kg CO2e. This matters and can be known.  The only way to convey this improvement about the product is to communicate the climate footprint with a relatively high precision, as the midpoint in the uncertainty interval. The uncertainty is outside of the control and knowledge of the producers and can from a probability perspective be assumed to affect the two products equally.

Important: Any comparison between products should only be made when the individual assessments have been made with the same method, scope, system boundaries and assumptions. If the different studies have been made with differences in any of these aspects the comparison may be unfair and unreliable, with the risk of the wrong conclusions being drawn. 

What does allocation mean and how does it work?

Allocation deals with the distribution of responsibility for emissions from a production systems that produce more than one final product.
A good example is a dairy cow, who produces milk, calves, meat, and leather. Throughout her life the cow causes emissions of greenhouse gases of various kinds. At the same time, she produces a number of calves, she produces milk, and finally she gets slaughtered which produces meat and leather. The meat in turn consists of higher and lower quality cuts. 

There is not one objective truth for how the emissions she caused throughout her life should be allocated between the products. Different allocations can be argued for to answer different questions. The result, unfortunately, is that comparisons of results between different LCA-studies for different products, such as different brands of cheese or milk may give an erroneous conclusions that there are differences where there are none, if the allocations were done differently in the different studies. This can be investigated, of course, but requires work. 

All allocations in CarbonData are done according to the same principles for all products, to make them internally fairly comparable.

What is the difference between climate footprint and CO2?

What you measure is climate footprint and the unit with which you measure it is kg CO2e, or only kg CO2 if all the emissions are carbon dioxide (CO2)Think about it as you would with length, where what you measure is the length and the unit you measure it with is meter. If it makes grammatical sense to write length you write climate footprint and if it makes grammatical sense to write meter then you write kg CO2e.

What does carbon dioxide equivalent (CO2e) mean?

There are many different greenhouse gases of which carbon dioxide is the most widely known. Different greenhouse gases affect the climate in different ways. Some stay in the atmosphere for a long time but do not cause so much warming per kg emissions, like carbon dioxide. Others, like methane, heat the earth a lot, but do not stay very long in the atmosphere. There is an exchange rate of sorts, that makes comparison of the different gases possible. The exchange rate expresses how many kg of carbon dioxide emissions that warms the climate equally as 1 kg of another greenhouse gas. The exchange rate is called Global Warming Potential and is typically abbreviated GWP. By knowing the GWP of different gases the total climate impact of a product can be condensed into one single unit: kilograms of carbon dioxide equivalents (kg CO2e).