Ok, I looked through the two references you provided, and additionally, one of the primary references by Walleczek (FEBS letters 271, 157-160, 1990). I can't comment fully, but here's my summary:
The two references you provided are review articles, not original research papers. I was unable to pull up the overwhelming majority of the original literature- I really wanted to read the Science articles, but they are not available online to my library, and the majority of journals referenced (Bioelectromagnetics, for example), I don't have access to at all.
I did pull up the FEBS letters article- an original research paper, and there are some (I feel) unresolved issues.
First, it's clear the magnetic field only affects Con-A treated cells. What is Con A? Con A is short of concanavalin A, and does not naturally occur in mammalian cells. I don't know much about it, but it does bind to Calcium and cell surface receptors- this is a very different mechanism than 'calcium uptake'. For example, the Con A could bind to extracellular calcium and then bind to the cell membrane.
In any case, the effect of the applied field (most likely) should be interpreted as a differential effect on Con A, not the cell- Figure 3 shows that conclusively.
Now, the applied field: they used a 22 T magnetic field, which is in excess of 10^6 times the Earth's magnetic field. So already, there is no physiological significance to the results. Then, they say the induced electric field goes as E = pi*f*r*B, where f is the frequency, and r the radius of the annual wire. I don't think that's correct: the relative intensities of the electric and magnetic field goes as B ~ E/c. This means that their claimed electric field magnitude of 1 mV/cm should really be about 10^8 mV/cm. This is *extremely* important, because the membrane potential is about 10^4 V/cm. According to their calculations, the applied field is a vanishing fraction of the membrane potential, when in fact the actual applied field is many times greater- the effect is to open transient pores in the membrane, allowing macromolecules to enter freely- this is the basis for electroporation, which I use to transfect cells all the time.
Thus, if the cells are in fact subjected to such a high field, many of the claimed results in the review articles can simply be attributed to electroporation and the effects of such a process- for example, extracellular Con A binds to the extracellular Ca, the complex flows into the cell as a result of electroporation, and thus the cells appear to have taken up a certain amount of Ca. Without seeing the articles about DNA and RNA transcription, I can't make definitive statements, but a similar mechanism could take place, especially if the applied field is so high.
So, while I don't dispute the data presented in the FEBS article, I do dispute the conclusions and interpretations, because their calculations are faulty.