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I have table of function f[x,a]. For the sake of easy reproduction, let's limit it to a few entries - the original is over 1000 x 1000:

actualtable=Table[f[x, a], {x, 0, 4}, {a, 1, 4}]
*{{f[0, 1], f[0, 2], f[0, 3], f[0, 4]}, {f[1, 1], f[1, 2], f[1, 3], 
f[1, 4]}, {f[2, 1], f[2, 2], f[2, 3], f[2, 4]}, {f[3, 1], f[3, 2], 
f[3, 3], f[3, 4]}, {f[4, 1], f[4, 2], f[4, 3], f[4, 4]}}*

I want to find a way to interject a value m between each list item, to create

desiredtable={{f[0, 1], m, f[0, 2], m, f[0, 3], m, f[0, 4]}, {f[1, 1], m, f[1, 2], 
m, f[1, 3], m, f[1, 4]}, {f[2, 1], m, f[2, 2], m, f[2, 3], m, 
f[2, 4]}, {f[3, 1], m, f[3, 2], m, f[3, 3], m, f[3, 4]}, {f[4, 1], 
m, f[4, 2], m, f[4, 3], m, f[4, 4]}}

I tried using Riffle in conjunction with Table, but it only injects m in between lines, rather than in between individual entries.

Obviously, with a tiny table like this, it's easy, I can just type in the ms, or type the Riffle command once for each line of the output.

But for a very big table, how do I do it?

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Map Riffle to each of the element of actualTable:

  desiredtable = Riffle[#, "m"] & /@ actualtable

(* {{f[0, 1], "m", f[0, 2], "m", f[0, 3], "m", f[0, 4]}, {f[1, 1], "m", f[1, 2], "m", f[1, 3], "m", f[1, 4]}, {f[2, 1], "m", f[2, 2], "m", f[2, 3], "m", f[2, 4]}, {f[3, 1], "m", f[3, 2], "m", f[3, 3], "m", f[3, 4]}, {f[4, 1], "m", f[4, 2], "m", f[4, 3], "m", f[4, 4]}}*)

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