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Hello, Herman!

You wrote: There is a little side error I guess 4’. What is max. permissible side error?

4' side error will produce about 0.3' error in measured angle. For traditional astronavigation it is nothing, but for lunars it is too much. I would recommend side error max 2'. This will produce about 0.06' error in lunar.  Small side error (less than  1') is acceptable. 

You wrote: Or is the little curved solarfilm (see photo) the cause of double sun?

Just try to measure IE using built-in filters (as already Tony recommended to you) and this will give you an answer on effect of the solarfilm. Compare these two methods.

Another test: do check the telescope focuss (try to change focus a little bit and look for changes in ghost image). 

I would like to say some words about filters directly on telescope. Tony wrote that by using built-in filters you take into considerations all the errors in these filters. I think that the problem is more complex.

When we measure IE by Sun, we use filters both on horizon and on index mirrors. But when we measure lunar distance, filters are only on one mirror (typicaly on index mirror) or filters are not used at all (star lunar distances). That means: filter combination is different for IE and for lunar distance measurment. And this fact can produce error of some tenths of the minute of arc. Therefore older sextants had special filters which  were used on telecope ocullar. For example, my Soviet sextant SNO-M has two such filters for telescope. Only using these filters it is possilble to avoid of built-in filter errors. You can obtain IE precisely, but this accuracy does not matter much if you use some filters during lunar observations. On one hand: you have accurat IE, on other hand: you measure lunars with filters of anknown error. Best solution: to measure error of filters. (My sextant in some filter combinations can produce additional error of 0.3').   

Modris