Regarding character design, the only ones I have trouble with at this time are both Itame and Princess Piña. Piña was converted from an adult twentysomething woman into a teenager girl. Itami now looks like your typical japanese otaku, i.e.: a creepy guy. Also, while Itami is indeed a slacker, he still does his job to the best of his abilities, something that we are not seeing here.
I do like that they are showing stuff that was time-skipped in the manga. The arrival of the JSDF and the first battle. We only say what happened with the combined army, but by that time the JSDF had already consolidated its position, built appropiate fortifications and firing position for its tanks. Brought some heavy duty AAA guns to deal with the dragons and was completely prepared to serve customers. At this time it is an expeditionary force that does not know what is going to happen. So we will get to see the 1st Battle of Alnus.
Regarding the gore and sex. I was really sure that it was going to be toned down as much as they could. No torn bodies but we see a lot of implied and some real blood. Violence was heavily implied since the camera was from the victim's perspective as opposed from an observer's viewpoint. Thus we saw the monsters attacking but not the deadly consequences. The little orphan girl that wasn't in the manga is to tell us that a lot of people died.
BTW, I don't think that Itami could have killed that guy with the knife the way he did it. The guy was wearing armor, very likely bronce, but it could have been boiled leather. Still that dinky knife wouldn't be able to penetrate that armor of his. So if he wanted to kill him, he would have had to cut his throat as opposed to knife him in the back.