Offhand, I honestly can't think of any examples of Third Reich symbolism and iconography used in the GDR.
As for the uniforms and insignia: It is worth noting that the earliest uniforms worn by the GDR's armed forces (i.e. the KVP as the forerunner of the NVA) were heavily influenced by Soviet style and had hardly any German design elements. The Soviet leadership was not universally enthusiastic about this; in fact, there is a famous anecdote illustrating the opposite: When attending the signing of the Warsaw Pact treaty in 1955 in his khaki uniform, the then-head of the KVP and later NVA Armeegeneral and government minister Heinz Hoffmann was taken aside by the Soviet Chairman of the Council of Minisiters and former Secretary of Defense Nikolai Bulganin, who asked him, in a clearly disapproving tone: "You are Germans, aren't you? Why don't you wear German uniforms, then?"
With the dawn of the NVA came new and very much German uniforms. The reason, in the words of the then-Generaloberst and subsequent Secretary of Defense Willi Stoph:
"With the National People's Army, a new uniform shall now be instituted as well; one that meets with the old German traditions of the national liberation armies. There can be no doubt that the West German mercenary formations, who are under American command, who have American uniforms, who are equipped with American weapons and are trained according to American methods, shall never be able to represent the intererests of the German people."
The service- and dress uniforms worn by the NVA may have seemed "Third Reich style" to the casual observer, but in fact, the models for all key design elements of these uniforms and insignia (the cut of the tunics, style and system of shoulder boards and collar patches, the dress aigullettes, the brocade belts, the high boots etc.) as well as the military ceremonial (including the goosestep) had been in existence long before the Nazi seizure of power in 1933.
The NVA very much understood itself as the keeper of old Germany military traditions and customs and - for all their Communist ideological background - embraced this role with pride and enthusiasm.
It was not for nothing that the NVA's highest military decoration, the Scharnhorst-Orden was named after one of the great Prussian military reformers and -thinkers, Gerhard von Scharnhorst, whereas its (never awarded) bravery decoration, the Blücher-Orden, was named in honor of legendary Prussian Field Marshal Gebhard Leberecht von Blücher.
(Amusingly, the only genuinely "Nazi" item of NVA kit was one that most members of the general public would not have suspected of being one: The NVA's steel helmet was essentially the final model of steel helmet developed for the Wehrmacht in WW2!)