Q: "Can I find the number e in the tables of Napier?"
"The number that I find on the last row of the last table is 3,465,735 rather than 3,678,794. Is there a number closer to e in the tables?"
To begin by cutting quickly to the chase, I see no mistake on Napier's part with the number 3465735 in the tables (which the question suggests is a mistake by Napier). When converted to modern form, with sign and decimal point, this number is at most 1 unit (in the last place) different from the natural-logarithmic sine (or cosine) of 45 degrees -- which is what it ought to be, for its place in the layout of Napier's tables.
John Napier of Merchistoun (various spellings survive) gave his first tables in his book with title 'Mirifici Logarithmorum Canonis Descriptio' (1614) -- translated four years later by Edward Wright as 'Description of the admirable table of logarithms'. Napier tabulated what can readily be recognized now as natural (or Napierian, or base-e) logarithms of trigonometric functions, but printed them according to conventions of his day, so that (for example) one does not look for decimal points or for signed numbers.
In the main tables, for example, each page-header gives an angle in degrees, and the successive rows are for functions of the header degree supplemented by 0, 1, 2, (etc) minutes. The first column of tabular values in any row then gives the (natural) sine of the angle for that row, and the second column gives the (natural, Napierian or base-e) logarithm of that sine. The remaining columns give natural-logarithmic tangent and cosine, then the natural cosine, and finally, on the right, the minutes in the complement to 90 degrees of the angle identified by the supplement of minutes in the left column (when the right-hand column angle is read as a supplement of minutes with the number of degrees shown this time at the foot of the table-page).
The result has an economy of layout, so that the tables as a whole appear to cover primarily a semi-quadrant (i.e. a range of 45 degrees). But when read in the appropriate direction for any chosen angle, i.e. downwards from the top and from left to right for angles in the range 0 to 45 degrees, but upwards from the foot and from right to left for angles in the range 45 to 90 degrees, they give the whole gamut of logarithmic sines, tangents, and cosines for an entire quadrant (thus also natural-logarithmic cotangents), although modern names (apart from 'sinus' and 'logarithmi') do not appear.
Although 8 digits are printed, the accuracy in those early tables does not always reach 6 digits e.g. relative to a precise natural-logarithmic sine value.
So, to the extent that one can find tabulated angles and the natural, base-e, logarithms of their sines and other trigonometric functions to the accuracy indicated, then yes, one can say that the base of the natural logarithms that we call 'e' is implicitly found there throughout.
One does not find the value of 'e' given explicitly in Napier's tables. But then it also doesn't appear explicitly in a modern table of natural logarithms or natural-logarithmic trig functions, either -- unless one counts its presence in a table of $e^x$, which is not strictly a logarithm table at all.
There can conceivably be other ways of looking at this question -- perhaps for example by asking whether there is a number close to but not equal to 'e', to which Napier's numerical values relate more closely than to 'e' itself. One could perhaps also say that in modern terms Napier has tabulated $-10^7 * ln (sin(angle))$ rather than the $ln(sin(angle))$ itself, and so on. But there does not seem to be evidence that Napier thought in ways that match either of those ideas. The non-modern way in which he did think can probably best be gathered through reading his description or at least its 17th-c. English translation.