The comment that mice are too fatty is commonly tossed about without regard to the metabolic needs of the frogs. Rodents are not too high in fat, they are typically offered too often by people who do not understand the metabolic needs of the frogs. They are calorically more dense so it is easier to over feed the frog on them (but then this can also occur with any food item offered to the frogs). In general, rodents compare favorably with insects with regard to the fat content.
Something from the archives I wrote awhile ago regarding the fat content in mice...
snip Actually house crickets contain 54% fat/kcal*, while commercial crickets contain 44% fat/kcal*, compared to 60% fat/kcal* for mealworms. Compared to a 1.5 gram pink which is 40% fat/kcal and an adult mouse (27 gram) which is 47% fat/kcal. Pinks do not take a jump in fat content until they are larger than 4 grams at which time they hit 60% fat/kcal which is no higher than mealworms.
The only low fat invertebrate that is commercially available are earthworms but a diet os solely earthworms has been linked to muscle diseases in anurans (see Modzelewski, E.H.; Culley, D.D. Jr.; 1974, Growth responses of the bull frog, Rana catesbiana, fed various live foods; Herpetologica, 30(4): 396-405)
* Donoghue, Susan; Langenberg, Julie, 1996, Nutrition, In Reptile Medicine and Surgery, edited by Mader, Douglas R., W.B. Saunders Company, Philadelphia "endsnip