Hm, I don't think warning 1 should appear if the situation is as you describe. Can you run:
```r
length(unique( my_big_data$Products ))
length(unique( my_subset_data$Products))
unique( my_subset_data$Products)[ ! (unique(my_subset_data$Products) %in% my_big_data$Products)]
```
And for the 2nd warning, that occurs when it finds multiple observations per Product and combination of conditions supplied to `within`. If the list provided to within is truly the full set of within-subject variables (i.e. you're not doing a follow-up analysis on a subset of the within-subject variables), then yes you can ignore that, but note that the existence of multiple measurements of this kind means that your data are actually of a "hierarchical" type and you are leaving information on the table by using anova versus a proper hierarchical modelling tool.