During the invasion of Normandy in 1944, how good was the Wehrmacht at that stage? Were there many experienced units stationed there or just second rate units? How much training did German soldiers have at that stage?
What about by the time of the battle of Hurtgen Forrest/Ardennes offensive? How big were the changes?
The German army in the west was very, very mixed. Broadly, you can break them down into three categories/levels of quality.
First, and lowest in quality, were the static (bodenstandig) infantry divisions, so named because they lacked the transportation to maneuver effectively and could only maintain defensive positions. The majority of the German troops guarding the long Atlantic Wall came from these divisions. Many had been in place for several years by this point, but due to the German practice of periodically stripping these divisions of their best men and officers to send to more active theaters (see: Russia), their manpower was highly variable and consisted of, in addition to ordinary German soldiers, overage men, convalescents, semi-invalids, ethnic Germans (volksdeutsche) from conquered countries, and eastern "volunteers" recruited from PoW camps and occupied Soviet territories. The one upshot was that they generally possessed an abundance of infantry support weapons, such as mortars, anti-tank guns, and obsolete tank turrets that had been installed as ersatz bunkers.
Occupying the middle tier would be the traditional German infantry divisions, theoretically capable of the full spectrum of infantry warfare. Probably the most famous of these to most readers will be the 352nd Infantry Division. This division can be looked at as a serviceable microcosm of the German infantry writ large. The 352nd was formed in late 1943 from the remnants of another division shattered in Russia. As such, the division had a cadre of battle-hardened officers and NCOs to build from, though there were never quite enough of them to go around. This shell was filled out with mostly new conscripts - 17- and 18-year-olds. Initially, it was planned that the division would return to Russia, and this influenced its course of training. It had a full complement of field artillery, which would play hell on Omaha Beach. However, the division had to split its time between training and constructing beach fortifications and anti-paratrooper obstacles, and the division officers felt they never were able to fully train the men. Nevertheless, it was an entirely more capable formation than, say, the 709th static division. However, it was very diluted in strength by the time of the landings. In accordance with an army-wide reorganization, the division had been pared from nine to six infantry battalions, two of which were in corps reserve, two of which were in local reserve, and only one of which was actually on Omaha Beach on 6 June. Now, the 352nd wasn't the only "regular" infantry division in Normandy, just the only one initially on-hand to combat the beach landings. More were rushed in as part of the German build-up.
The mobile divisions - that is, the armored and mechanized divisions - were undoubtedly the strongest, best-equipped formations in the German Army. They received the best personnel and were freed from the obligations of beach fortification and garrison duty. Only one, the 21st Panzer Division, was in the Normandy area on 6 June, but ten additional divisions were committed over the course of the battle. These elite mobile divisions stunted the British at Caen, but paid a very heavy price for their efforts. They were almost totally destroyed during the Allied breakout, to the great weakening of the German Army in the west. In the aftermath of their mauling, hurriedly formed panzerbrigades were rushed west to attempt to halt the onrushing Allies, but these formations lacked experience, a proper balance of combined arms, and were roughly handled by the large veteran American tank divisions in fall 1944.