Urinary Tract Infection (UTI) or Pneumonia leading to anemia: Given the patient's age, a UTI or pneumonia could easily lead to anemia due to chronic blood loss or inflammation, and hematuria can be a symptom of a UTI.

Bladder Cancer: Hematuria is a common presenting symptom of bladder cancer, especially in older adults.
Kidney Stones: While more common in younger populations, kidney stones can still occur in the elderly and cause hematuria and potentially anemia if there's significant blood loss.
Benign Prostatic Hyperplasia (BPH) or other obstructive uropathy: In women, less common than in men, but any obstructive process can lead to urinary retention, infection, and potentially hematuria and anemia.

Renal Cell Carcinoma: Although less likely than bladder cancer, renal cell carcinoma can present with hematuria and anemia, and missing this diagnosis could be fatal.
Vasculitis (e.g., ANCA-associated vasculitis): Certain types of vasculitis can present with renal involvement, leading to hematuria and anemia, and are critical to diagnose due to their potential for severe morbidity and mortality.
Sickle Cell Disease crisis: Though less common in an 80-year-old, if the patient has sickle cell disease, a crisis could lead to anemia and hematuria.

Goodpasture Syndrome: An autoimmune disease that can cause renal failure and hematuria, though it's rare and more commonly seen in younger populations.
Alport Syndrome: A genetic disorder affecting the type IV collagen in the kidneys, leading to hematuria, but typically presents earlier in life.
Tubulointerstitial Nephritis: Can cause hematuria and anemia but is less common and often associated with specific drug exposures or infections.